This batch has passed Schema, deduplication, source-snapshot, and independent-answer recomputation checks; it is still not marked as human-reviewed.
This question bank has corresponding bilingual step-by-step derivations. Source candidate and English ai_candidate states are retained. AI review, finite computation and Lean formal proof are labelled separately.
batch-20260927-linear-equation-foundations · 2026-09-27 · 100 questions
This English edition is an AI candidate and does not yet have an OCME Atlas (GPT-6) Twin closure receipt.
Over the rational numbers, consider 0x+(-12)=0. Under this MKO, is it a linear equation in one variable?
No
a=0, so this is a degenerate constant equation rather than a linear equation in one variable.
Reviewed step-by-step derivation
Linear equation in one variable · qf-linear-equation-form-validity · candidate
Over the rational numbers, consider -3x+(-11)=0. Under this MKO, is it a linear equation in one variable?
Yes
a=-3≠0, so this is a linear equation in one variable under the MKO definition.
Reviewed step-by-step derivation
Linear equation in one variable · qf-linear-equation-form-validity · candidate
Over the rational numbers, consider -2x+(-10)=0. Under this MKO, is it a linear equation in one variable?
Yes
a=-2≠0, so this is a linear equation in one variable under the MKO definition.
Reviewed step-by-step derivation
Linear equation in one variable · qf-linear-equation-form-validity · candidate
Over the rational numbers, consider -1x+(-9)=0. Under this MKO, is it a linear equation in one variable?
Yes
a=-1≠0, so this is a linear equation in one variable under the MKO definition.
Reviewed step-by-step derivation
Linear equation in one variable · qf-linear-equation-form-validity · candidate
Over the rational numbers, consider 1x+(-8)=0. Under this MKO, is it a linear equation in one variable?
Yes
a=1≠0, so this is a linear equation in one variable under the MKO definition.
Reviewed step-by-step derivation
Linear equation in one variable · qf-linear-equation-form-validity · candidate
Over the rational numbers, consider 0x+(-7)=0. Under this MKO, is it a linear equation in one variable?
No
a=0, so this is a degenerate constant equation rather than a linear equation in one variable.
Reviewed step-by-step derivation
Linear equation in one variable · qf-linear-equation-form-validity · candidate
Over the rational numbers, consider 2x+(-6)=0. Under this MKO, is it a linear equation in one variable?
Yes
a=2≠0, so this is a linear equation in one variable under the MKO definition.
Reviewed step-by-step derivation
Linear equation in one variable · qf-linear-equation-form-validity · candidate
Over the rational numbers, consider 3x+(-5)=0. Under this MKO, is it a linear equation in one variable?
Yes
a=3≠0, so this is a linear equation in one variable under the MKO definition.
Reviewed step-by-step derivation
Linear equation in one variable · qf-linear-equation-form-validity · candidate
Over the rational numbers, consider 4x+(-4)=0. Under this MKO, is it a linear equation in one variable?
Yes
a=4≠0, so this is a linear equation in one variable under the MKO definition.
Reviewed step-by-step derivation
Linear equation in one variable · qf-linear-equation-form-validity · candidate
Over the rational numbers, consider -4x+(-3)=0. Under this MKO, is it a linear equation in one variable?
Yes
a=-4≠0, so this is a linear equation in one variable under the MKO definition.
Reviewed step-by-step derivation
Linear equation in one variable · qf-linear-equation-form-validity · candidate
Over the rational numbers, consider 0x+(-2)=0. Under this MKO, is it a linear equation in one variable?
No
a=0, so this is a degenerate constant equation rather than a linear equation in one variable.
Reviewed step-by-step derivation
Linear equation in one variable · qf-linear-equation-form-validity · candidate
Over the rational numbers, consider -2x+(-1)=0. Under this MKO, is it a linear equation in one variable?
Yes
a=-2≠0, so this is a linear equation in one variable under the MKO definition.
Reviewed step-by-step derivation
Linear equation in one variable · qf-linear-equation-form-validity · candidate
Over the rational numbers, consider -1x+(0)=0. Under this MKO, is it a linear equation in one variable?
Yes
a=-1≠0, so this is a linear equation in one variable under the MKO definition.
Reviewed step-by-step derivation
Linear equation in one variable · qf-linear-equation-form-validity · candidate
Over the rational numbers, consider 1x+(1)=0. Under this MKO, is it a linear equation in one variable?
Yes
a=1≠0, so this is a linear equation in one variable under the MKO definition.
Reviewed step-by-step derivation
Linear equation in one variable · qf-linear-equation-form-validity · candidate
Over the rational numbers, consider 1x+(2)=0. Under this MKO, is it a linear equation in one variable?
Yes
a=1≠0, so this is a linear equation in one variable under the MKO definition.
Reviewed step-by-step derivation
Linear equation in one variable · qf-linear-equation-form-validity · candidate
Over the rational numbers, consider 0x+(3)=0. Under this MKO, is it a linear equation in one variable?
No
a=0, so this is a degenerate constant equation rather than a linear equation in one variable.
Reviewed step-by-step derivation
Linear equation in one variable · qf-linear-equation-form-validity · candidate
Over the rational numbers, consider 3x+(4)=0. Under this MKO, is it a linear equation in one variable?
Yes
a=3≠0, so this is a linear equation in one variable under the MKO definition.
Reviewed step-by-step derivation
Linear equation in one variable · qf-linear-equation-form-validity · candidate
Over the rational numbers, consider 4x+(5)=0. Under this MKO, is it a linear equation in one variable?
Yes
a=4≠0, so this is a linear equation in one variable under the MKO definition.
Reviewed step-by-step derivation
Linear equation in one variable · qf-linear-equation-form-validity · candidate
Over the rational numbers, consider -4x+(6)=0. Under this MKO, is it a linear equation in one variable?
Yes
a=-4≠0, so this is a linear equation in one variable under the MKO definition.
Reviewed step-by-step derivation
Linear equation in one variable · qf-linear-equation-form-validity · candidate
Over the rational numbers, consider -3x+(7)=0. Under this MKO, is it a linear equation in one variable?
Yes
a=-3≠0, so this is a linear equation in one variable under the MKO definition.
Reviewed step-by-step derivation
Linear equation in one variable · qf-linear-equation-form-validity · candidate
Over the rational numbers, consider 0x+(8)=0. Under this MKO, is it a linear equation in one variable?
No
a=0, so this is a degenerate constant equation rather than a linear equation in one variable.
Reviewed step-by-step derivation
Linear equation in one variable · qf-linear-equation-form-validity · candidate
Over the rational numbers, consider -1x+(9)=0. Under this MKO, is it a linear equation in one variable?
Yes
a=-1≠0, so this is a linear equation in one variable under the MKO definition.
Reviewed step-by-step derivation
Linear equation in one variable · qf-linear-equation-form-validity · candidate
Over the rational numbers, consider 1x+(10)=0. Under this MKO, is it a linear equation in one variable?
Yes
a=1≠0, so this is a linear equation in one variable under the MKO definition.
Reviewed step-by-step derivation
Linear equation in one variable · qf-linear-equation-form-validity · candidate
Over the rational numbers, consider 1x+(11)=0. Under this MKO, is it a linear equation in one variable?
Yes
a=1≠0, so this is a linear equation in one variable under the MKO definition.
Reviewed step-by-step derivation
Linear equation in one variable · qf-linear-equation-form-validity · candidate
Over the rational numbers, consider 2x+(12)=0. Under this MKO, is it a linear equation in one variable?
Yes
a=2≠0, so this is a linear equation in one variable under the MKO definition.
Reviewed step-by-step derivation
Linear equation in one variable · qf-linear-equation-form-validity · candidate
Solve -5x+(-15)=0 exactly over the rational numbers; a=-5 is explicitly nonzero.
-3
x=−(-15)/-5=-3; the result is reduced by the gcd to a canonical rational with a positive denominator.
Reviewed step-by-step derivation
Linear equation in one variable · qf-linear-equation-exact-solve · candidate
Solve -4x+(-8)=0 exactly over the rational numbers; a=-4 is explicitly nonzero.
-2
x=−(-8)/-4=-2; the result is reduced by the gcd to a canonical rational with a positive denominator.
Reviewed step-by-step derivation
Linear equation in one variable · qf-linear-equation-exact-solve · candidate
Solve -3x+(-1)=0 exactly over the rational numbers; a=-3 is explicitly nonzero.
-1/3
x=−(-1)/-3=-1/3; the result is reduced by the gcd to a canonical rational with a positive denominator.
Reviewed step-by-step derivation
Linear equation in one variable · qf-linear-equation-exact-solve · candidate
Solve -2x+(6)=0 exactly over the rational numbers; a=-2 is explicitly nonzero.
3
x=−(6)/-2=3; the result is reduced by the gcd to a canonical rational with a positive denominator.
Reviewed step-by-step derivation
Linear equation in one variable · qf-linear-equation-exact-solve · candidate
Solve -1x+(13)=0 exactly over the rational numbers; a=-1 is explicitly nonzero.
13
x=−(13)/-1=13; the result is reduced by the gcd to a canonical rational with a positive denominator.
Reviewed step-by-step derivation
Linear equation in one variable · qf-linear-equation-exact-solve · candidate
Solve 1x+(-11)=0 exactly over the rational numbers; a=1 is explicitly nonzero.
11
x=−(-11)/1=11; the result is reduced by the gcd to a canonical rational with a positive denominator.
Reviewed step-by-step derivation
Linear equation in one variable · qf-linear-equation-exact-solve · candidate
Solve 1x+(-4)=0 exactly over the rational numbers; a=1 is explicitly nonzero.
4
x=−(-4)/1=4; the result is reduced by the gcd to a canonical rational with a positive denominator.
Reviewed step-by-step derivation
Linear equation in one variable · qf-linear-equation-exact-solve · candidate
Solve 2x+(3)=0 exactly over the rational numbers; a=2 is explicitly nonzero.
-3/2
x=−(3)/2=-3/2; the result is reduced by the gcd to a canonical rational with a positive denominator.
Reviewed step-by-step derivation
Linear equation in one variable · qf-linear-equation-exact-solve · candidate
Solve 3x+(10)=0 exactly over the rational numbers; a=3 is explicitly nonzero.
-10/3
x=−(10)/3=-10/3; the result is reduced by the gcd to a canonical rational with a positive denominator.
Reviewed step-by-step derivation
Linear equation in one variable · qf-linear-equation-exact-solve · candidate
Solve 4x+(-14)=0 exactly over the rational numbers; a=4 is explicitly nonzero.
7/2
x=−(-14)/4=7/2; the result is reduced by the gcd to a canonical rational with a positive denominator.
Reviewed step-by-step derivation
Linear equation in one variable · qf-linear-equation-exact-solve · candidate
Solve 5x+(-7)=0 exactly over the rational numbers; a=5 is explicitly nonzero.
7/5
x=−(-7)/5=7/5; the result is reduced by the gcd to a canonical rational with a positive denominator.
Reviewed step-by-step derivation
Linear equation in one variable · qf-linear-equation-exact-solve · candidate
Solve -5x+(0)=0 exactly over the rational numbers; a=-5 is explicitly nonzero.
0
x=−(0)/-5=0; the result is reduced by the gcd to a canonical rational with a positive denominator.
Reviewed step-by-step derivation
Linear equation in one variable · qf-linear-equation-exact-solve · candidate
Solve -4x+(7)=0 exactly over the rational numbers; a=-4 is explicitly nonzero.
7/4
x=−(7)/-4=7/4; the result is reduced by the gcd to a canonical rational with a positive denominator.
Reviewed step-by-step derivation
Linear equation in one variable · qf-linear-equation-exact-solve · candidate
Solve -3x+(14)=0 exactly over the rational numbers; a=-3 is explicitly nonzero.
14/3
x=−(14)/-3=14/3; the result is reduced by the gcd to a canonical rational with a positive denominator.
Reviewed step-by-step derivation
Linear equation in one variable · qf-linear-equation-exact-solve · candidate
Solve -2x+(-10)=0 exactly over the rational numbers; a=-2 is explicitly nonzero.
-5
x=−(-10)/-2=-5; the result is reduced by the gcd to a canonical rational with a positive denominator.
Reviewed step-by-step derivation
Linear equation in one variable · qf-linear-equation-exact-solve · candidate
Solve -1x+(-3)=0 exactly over the rational numbers; a=-1 is explicitly nonzero.
-3
x=−(-3)/-1=-3; the result is reduced by the gcd to a canonical rational with a positive denominator.
Reviewed step-by-step derivation
Linear equation in one variable · qf-linear-equation-exact-solve · candidate
Solve 1x+(4)=0 exactly over the rational numbers; a=1 is explicitly nonzero.
-4
x=−(4)/1=-4; the result is reduced by the gcd to a canonical rational with a positive denominator.
Reviewed step-by-step derivation
Linear equation in one variable · qf-linear-equation-exact-solve · candidate
Solve 1x+(11)=0 exactly over the rational numbers; a=1 is explicitly nonzero.
-11
x=−(11)/1=-11; the result is reduced by the gcd to a canonical rational with a positive denominator.
Reviewed step-by-step derivation
Linear equation in one variable · qf-linear-equation-exact-solve · candidate
Solve 2x+(-13)=0 exactly over the rational numbers; a=2 is explicitly nonzero.
13/2
x=−(-13)/2=13/2; the result is reduced by the gcd to a canonical rational with a positive denominator.
Reviewed step-by-step derivation
Linear equation in one variable · qf-linear-equation-exact-solve · candidate
Solve 3x+(-6)=0 exactly over the rational numbers; a=3 is explicitly nonzero.
2
x=−(-6)/3=2; the result is reduced by the gcd to a canonical rational with a positive denominator.
Reviewed step-by-step derivation
Linear equation in one variable · qf-linear-equation-exact-solve · candidate
Solve 4x+(1)=0 exactly over the rational numbers; a=4 is explicitly nonzero.
-1/4
x=−(1)/4=-1/4; the result is reduced by the gcd to a canonical rational with a positive denominator.
Reviewed step-by-step derivation
Linear equation in one variable · qf-linear-equation-exact-solve · candidate
Solve 5x+(8)=0 exactly over the rational numbers; a=5 is explicitly nonzero.
-8/5
x=−(8)/5=-8/5; the result is reduced by the gcd to a canonical rational with a positive denominator.
Reviewed step-by-step derivation
Linear equation in one variable · qf-linear-equation-exact-solve · candidate
Solve -5x+(15)=0 exactly over the rational numbers; a=-5 is explicitly nonzero.
3
x=−(15)/-5=3; the result is reduced by the gcd to a canonical rational with a positive denominator.
Reviewed step-by-step derivation
Linear equation in one variable · qf-linear-equation-exact-solve · candidate
Solve -4x+(-9)=0 exactly over the rational numbers; a=-4 is explicitly nonzero.
-9/4
x=−(-9)/-4=-9/4; the result is reduced by the gcd to a canonical rational with a positive denominator.
Reviewed step-by-step derivation
Linear equation in one variable · qf-linear-equation-exact-solve · candidate
Solve -3x+(-2)=0 exactly over the rational numbers; a=-3 is explicitly nonzero.
-2/3
x=−(-2)/-3=-2/3; the result is reduced by the gcd to a canonical rational with a positive denominator.
Reviewed step-by-step derivation
Linear equation in one variable · qf-linear-equation-exact-solve · candidate
Over the rational numbers, consider -4x+(-14)=0 and the candidate x=-7/2. Is the candidate a solution?
Yes
q=2≠0 and -4×-7+(-14)×2=0, so the candidate is a solution.
Reviewed step-by-step derivation
Linear equation in one variable · qf-linear-equation-solution-verification · candidate
Over the rational numbers, consider -3x+(-9)=0 and the candidate x=-2/1. Is the candidate a solution?
No
q=1≠0 and -3×-2+(-9)×1=-3, so the candidate is not a solution.
Reviewed step-by-step derivation
Linear equation in one variable · qf-linear-equation-solution-verification · candidate
Over the rational numbers, consider -2x+(-4)=0 and the candidate x=-2/1. Is the candidate a solution?
Yes
q=1≠0 and -2×-2+(-4)×1=0, so the candidate is a solution.
Reviewed step-by-step derivation
Linear equation in one variable · qf-linear-equation-solution-verification · candidate
Over the rational numbers, consider -1x+(1)=0 and the candidate x=2/1. Is the candidate a solution?
No
q=1≠0 and -1×2+(1)×1=-1, so the candidate is not a solution.
Reviewed step-by-step derivation
Linear equation in one variable · qf-linear-equation-solution-verification · candidate
Over the rational numbers, consider 2x+(6)=0 and the candidate x=-3/1. Is the candidate a solution?
Yes
q=1≠0 and 2×-3+(6)×1=0, so the candidate is a solution.
Reviewed step-by-step derivation
Linear equation in one variable · qf-linear-equation-solution-verification · candidate
Over the rational numbers, consider 1x+(11)=0 and the candidate x=-10/1. Is the candidate a solution?
No
q=1≠0 and 1×-10+(11)×1=1, so the candidate is not a solution.
Reviewed step-by-step derivation
Linear equation in one variable · qf-linear-equation-solution-verification · candidate
Over the rational numbers, consider 2x+(-13)=0 and the candidate x=13/2. Is the candidate a solution?
Yes
q=2≠0 and 2×13+(-13)×2=0, so the candidate is a solution.
Reviewed step-by-step derivation
Linear equation in one variable · qf-linear-equation-solution-verification · candidate
Over the rational numbers, consider 3x+(-8)=0 and the candidate x=3/1. Is the candidate a solution?
No
q=1≠0 and 3×3+(-8)×1=1, so the candidate is not a solution.
Reviewed step-by-step derivation
Linear equation in one variable · qf-linear-equation-solution-verification · candidate
Over the rational numbers, consider 4x+(-3)=0 and the candidate x=3/4. Is the candidate a solution?
Yes
q=4≠0 and 4×3+(-3)×4=0, so the candidate is a solution.
Reviewed step-by-step derivation
Linear equation in one variable · qf-linear-equation-solution-verification · candidate
Over the rational numbers, consider -4x+(2)=0 and the candidate x=1/1. Is the candidate a solution?
No
q=1≠0 and -4×1+(2)×1=-2, so the candidate is not a solution.
Reviewed step-by-step derivation
Linear equation in one variable · qf-linear-equation-solution-verification · candidate
Over the rational numbers, consider -3x+(7)=0 and the candidate x=7/3. Is the candidate a solution?
Yes
q=3≠0 and -3×7+(7)×3=0, so the candidate is a solution.
Reviewed step-by-step derivation
Linear equation in one variable · qf-linear-equation-solution-verification · candidate
Over the rational numbers, consider -2x+(12)=0 and the candidate x=7/1. Is the candidate a solution?
No
q=1≠0 and -2×7+(12)×1=-2, so the candidate is not a solution.
Reviewed step-by-step derivation
Linear equation in one variable · qf-linear-equation-solution-verification · candidate
Over the rational numbers, consider -1x+(-12)=0 and the candidate x=-12/1. Is the candidate a solution?
Yes
q=1≠0 and -1×-12+(-12)×1=0, so the candidate is a solution.
Reviewed step-by-step derivation
Linear equation in one variable · qf-linear-equation-solution-verification · candidate
Over the rational numbers, consider 2x+(-7)=0 and the candidate x=4/1. Is the candidate a solution?
No
q=1≠0 and 2×4+(-7)×1=1, so the candidate is not a solution.
Reviewed step-by-step derivation
Linear equation in one variable · qf-linear-equation-solution-verification · candidate
Over the rational numbers, consider 1x+(-2)=0 and the candidate x=2/1. Is the candidate a solution?
Yes
q=1≠0 and 1×2+(-2)×1=0, so the candidate is a solution.
Reviewed step-by-step derivation
Linear equation in one variable · qf-linear-equation-solution-verification · candidate
Over the rational numbers, consider 2x+(3)=0 and the candidate x=-1/1. Is the candidate a solution?
No
q=1≠0 and 2×-1+(3)×1=1, so the candidate is not a solution.
Reviewed step-by-step derivation
Linear equation in one variable · qf-linear-equation-solution-verification · candidate
Over the rational numbers, consider 3x+(8)=0 and the candidate x=-8/3. Is the candidate a solution?
Yes
q=3≠0 and 3×-8+(8)×3=0, so the candidate is a solution.
Reviewed step-by-step derivation
Linear equation in one variable · qf-linear-equation-solution-verification · candidate
Over the rational numbers, consider 4x+(13)=0 and the candidate x=-3/1. Is the candidate a solution?
No
q=1≠0 and 4×-3+(13)×1=1, so the candidate is not a solution.
Reviewed step-by-step derivation
Linear equation in one variable · qf-linear-equation-solution-verification · candidate
Over the rational numbers, consider -4x+(-11)=0 and the candidate x=-11/4. Is the candidate a solution?
Yes
q=4≠0 and -4×-11+(-11)×4=0, so the candidate is a solution.
Reviewed step-by-step derivation
Linear equation in one variable · qf-linear-equation-solution-verification · candidate
Over the rational numbers, consider -3x+(-6)=0 and the candidate x=-1/1. Is the candidate a solution?
No
q=1≠0 and -3×-1+(-6)×1=-3, so the candidate is not a solution.
Reviewed step-by-step derivation
Linear equation in one variable · qf-linear-equation-solution-verification · candidate
Over the rational numbers, consider -2x+(-1)=0 and the candidate x=-1/2. Is the candidate a solution?
Yes
q=2≠0 and -2×-1+(-1)×2=0, so the candidate is a solution.
Reviewed step-by-step derivation
Linear equation in one variable · qf-linear-equation-solution-verification · candidate
Over the rational numbers, consider -1x+(4)=0 and the candidate x=5/1. Is the candidate a solution?
No
q=1≠0 and -1×5+(4)×1=-1, so the candidate is not a solution.
Reviewed step-by-step derivation
Linear equation in one variable · qf-linear-equation-solution-verification · candidate
Over the rational numbers, consider 2x+(9)=0 and the candidate x=-9/2. Is the candidate a solution?
Yes
q=2≠0 and 2×-9+(9)×2=0, so the candidate is a solution.
Reviewed step-by-step derivation
Linear equation in one variable · qf-linear-equation-solution-verification · candidate
Over the rational numbers, consider 1x+(14)=0 and the candidate x=-13/1. Is the candidate a solution?
No
q=1≠0 and 1×-13+(14)×1=1, so the candidate is not a solution.
Reviewed step-by-step derivation
Linear equation in one variable · qf-linear-equation-solution-verification · candidate
Over the rational numbers, consider 2x+(-10)=0 and the candidate x=5/1. Is the candidate a solution?
Yes
q=1≠0 and 2×5+(-10)×1=0, so the candidate is a solution.
Reviewed step-by-step derivation
Linear equation in one variable · qf-linear-equation-solution-verification · candidate
Over the rational numbers, classify the solution set of 0x+(0)=0.
all rational numbers are solutions
With a=0 and b=0, the equation is 0=0, so every rational number is a solution.
Reviewed step-by-step derivation
Linear equation in one variable · qf-linear-equation-solution-class · candidate
Over the rational numbers, classify the solution set of 0x+(1)=0.
no solution
With a=0 and b=1≠0, the equation is 1=0, so it has no solution.
Reviewed step-by-step derivation
Linear equation in one variable · qf-linear-equation-solution-class · candidate
Over the rational numbers, classify the solution set of 0x+(2)=0.
no solution
With a=0 and b=2≠0, the equation is 2=0, so it has no solution.
Reviewed step-by-step derivation
Linear equation in one variable · qf-linear-equation-solution-class · candidate
Over the rational numbers, classify the solution set of 0x+(3)=0.
no solution
With a=0 and b=3≠0, the equation is 3=0, so it has no solution.
Reviewed step-by-step derivation
Linear equation in one variable · qf-linear-equation-solution-class · candidate
Over the rational numbers, classify the solution set of 0x+(4)=0.
no solution
With a=0 and b=4≠0, the equation is 4=0, so it has no solution.
Reviewed step-by-step derivation
Linear equation in one variable · qf-linear-equation-solution-class · candidate
Over the rational numbers, classify the solution set of 0x+(5)=0.
no solution
With a=0 and b=5≠0, the equation is 5=0, so it has no solution.
Reviewed step-by-step derivation
Linear equation in one variable · qf-linear-equation-solution-class · candidate
Over the rational numbers, classify the solution set of 0x+(6)=0.
no solution
With a=0 and b=6≠0, the equation is 6=0, so it has no solution.
Reviewed step-by-step derivation
Linear equation in one variable · qf-linear-equation-solution-class · candidate
Over the rational numbers, classify the solution set of 0x+(7)=0.
no solution
With a=0 and b=7≠0, the equation is 7=0, so it has no solution.
Reviewed step-by-step derivation
Linear equation in one variable · qf-linear-equation-solution-class · candidate
Over the rational numbers, classify the solution set of 0x+(8)=0.
no solution
With a=0 and b=8≠0, the equation is 8=0, so it has no solution.
Reviewed step-by-step derivation
Linear equation in one variable · qf-linear-equation-solution-class · candidate
Over the rational numbers, classify the solution set of 3x+(-3)=0.
unique solution x=1
Because a=3≠0, the equation has the unique solution x=1.
Reviewed step-by-step derivation
Linear equation in one variable · qf-linear-equation-solution-class · candidate
Over the rational numbers, classify the solution set of 4x+(-2)=0.
unique solution x=1/2
Because a=4≠0, the equation has the unique solution x=1/2.
Reviewed step-by-step derivation
Linear equation in one variable · qf-linear-equation-solution-class · candidate
Over the rational numbers, classify the solution set of 5x+(-1)=0.
unique solution x=1/5
Because a=5≠0, the equation has the unique solution x=1/5.
Reviewed step-by-step derivation
Linear equation in one variable · qf-linear-equation-solution-class · candidate
Over the rational numbers, classify the solution set of 6x+(0)=0.
unique solution x=0
Because a=6≠0, the equation has the unique solution x=0.
Reviewed step-by-step derivation
Linear equation in one variable · qf-linear-equation-solution-class · candidate
Over the rational numbers, classify the solution set of 7x+(1)=0.
unique solution x=-1/7
Because a=7≠0, the equation has the unique solution x=-1/7.
Reviewed step-by-step derivation
Linear equation in one variable · qf-linear-equation-solution-class · candidate
Over the rational numbers, classify the solution set of 1x+(2)=0.
unique solution x=-2
Because a=1≠0, the equation has the unique solution x=-2.
Reviewed step-by-step derivation
Linear equation in one variable · qf-linear-equation-solution-class · candidate
Over the rational numbers, classify the solution set of 2x+(3)=0.
unique solution x=-3/2
Because a=2≠0, the equation has the unique solution x=-3/2.
Reviewed step-by-step derivation
Linear equation in one variable · qf-linear-equation-solution-class · candidate
Over the rational numbers, classify the solution set of 3x+(4)=0.
unique solution x=-4/3
Because a=3≠0, the equation has the unique solution x=-4/3.
Reviewed step-by-step derivation
Linear equation in one variable · qf-linear-equation-solution-class · candidate
Over the rational numbers, classify the solution set of 4x+(5)=0.
unique solution x=-5/4
Because a=4≠0, the equation has the unique solution x=-5/4.
Reviewed step-by-step derivation
Linear equation in one variable · qf-linear-equation-solution-class · candidate
Over the rational numbers, classify the solution set of 5x+(6)=0.
unique solution x=-6/5
Because a=5≠0, the equation has the unique solution x=-6/5.
Reviewed step-by-step derivation
Linear equation in one variable · qf-linear-equation-solution-class · candidate
Over the rational numbers, classify the solution set of 6x+(7)=0.
unique solution x=-7/6
Because a=6≠0, the equation has the unique solution x=-7/6.
Reviewed step-by-step derivation
Linear equation in one variable · qf-linear-equation-solution-class · candidate
Over the rational numbers, classify the solution set of 7x+(8)=0.
unique solution x=-8/7
Because a=7≠0, the equation has the unique solution x=-8/7.
Reviewed step-by-step derivation
Linear equation in one variable · qf-linear-equation-solution-class · candidate
Over the rational numbers, classify the solution set of 1x+(9)=0.
unique solution x=-9
Because a=1≠0, the equation has the unique solution x=-9.
Reviewed step-by-step derivation
Linear equation in one variable · qf-linear-equation-solution-class · candidate
Over the rational numbers, classify the solution set of 2x+(10)=0.
unique solution x=-5
Because a=2≠0, the equation has the unique solution x=-5.
Reviewed step-by-step derivation
Linear equation in one variable · qf-linear-equation-solution-class · candidate
Over the rational numbers, classify the solution set of 3x+(11)=0.
unique solution x=-11/3
Because a=3≠0, the equation has the unique solution x=-11/3.
Reviewed step-by-step derivation
Linear equation in one variable · qf-linear-equation-solution-class · candidate
Over the rational numbers, classify the solution set of 4x+(12)=0.
unique solution x=-3
Because a=4≠0, the equation has the unique solution x=-3.
Reviewed step-by-step derivation
Linear equation in one variable · qf-linear-equation-solution-class · candidate
Canonical question JSONL · English JSONL · Validation report