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-20260928-absolute-value-foundations · 2026-09-28 · 100 questions
This English edition is an AI candidate and does not yet have an OCME Atlas (GPT-6) Twin closure receipt.
Using the piecewise definition over the real numbers, compute |-12| exactly.
12
-12<0, so absolute value takes the additive inverse and |-12|=12.
Reviewed step-by-step derivation
Absolute value · qf-absolute-value-exact-evaluation · candidate
Using the piecewise definition over the real numbers, compute |-11| exactly.
11
-11<0, so absolute value takes the additive inverse and |-11|=11.
Reviewed step-by-step derivation
Absolute value · qf-absolute-value-exact-evaluation · candidate
Using the piecewise definition over the real numbers, compute |-10| exactly.
10
-10<0, so absolute value takes the additive inverse and |-10|=10.
Reviewed step-by-step derivation
Absolute value · qf-absolute-value-exact-evaluation · candidate
Using the piecewise definition over the real numbers, compute |-9| exactly.
9
-9<0, so absolute value takes the additive inverse and |-9|=9.
Reviewed step-by-step derivation
Absolute value · qf-absolute-value-exact-evaluation · candidate
Using the piecewise definition over the real numbers, compute |-8| exactly.
8
-8<0, so absolute value takes the additive inverse and |-8|=8.
Reviewed step-by-step derivation
Absolute value · qf-absolute-value-exact-evaluation · candidate
Using the piecewise definition over the real numbers, compute |-7| exactly.
7
-7<0, so absolute value takes the additive inverse and |-7|=7.
Reviewed step-by-step derivation
Absolute value · qf-absolute-value-exact-evaluation · candidate
Using the piecewise definition over the real numbers, compute |-6| exactly.
6
-6<0, so absolute value takes the additive inverse and |-6|=6.
Reviewed step-by-step derivation
Absolute value · qf-absolute-value-exact-evaluation · candidate
Using the piecewise definition over the real numbers, compute |-5| exactly.
5
-5<0, so absolute value takes the additive inverse and |-5|=5.
Reviewed step-by-step derivation
Absolute value · qf-absolute-value-exact-evaluation · candidate
Using the piecewise definition over the real numbers, compute |-4| exactly.
4
-4<0, so absolute value takes the additive inverse and |-4|=4.
Reviewed step-by-step derivation
Absolute value · qf-absolute-value-exact-evaluation · candidate
Using the piecewise definition over the real numbers, compute |-3| exactly.
3
-3<0, so absolute value takes the additive inverse and |-3|=3.
Reviewed step-by-step derivation
Absolute value · qf-absolute-value-exact-evaluation · candidate
Using the piecewise definition over the real numbers, compute |-2| exactly.
2
-2<0, so absolute value takes the additive inverse and |-2|=2.
Reviewed step-by-step derivation
Absolute value · qf-absolute-value-exact-evaluation · candidate
Using the piecewise definition over the real numbers, compute |-1| exactly.
1
-1<0, so absolute value takes the additive inverse and |-1|=1.
Reviewed step-by-step derivation
Absolute value · qf-absolute-value-exact-evaluation · candidate
Using the piecewise definition over the real numbers, compute |0| exactly.
0
0≥0, so absolute value keeps the input and |0|=0.
Reviewed step-by-step derivation
Absolute value · qf-absolute-value-exact-evaluation · candidate
Using the piecewise definition over the real numbers, compute |1| exactly.
1
1≥0, so absolute value keeps the input and |1|=1.
Reviewed step-by-step derivation
Absolute value · qf-absolute-value-exact-evaluation · candidate
Using the piecewise definition over the real numbers, compute |2| exactly.
2
2≥0, so absolute value keeps the input and |2|=2.
Reviewed step-by-step derivation
Absolute value · qf-absolute-value-exact-evaluation · candidate
Using the piecewise definition over the real numbers, compute |3| exactly.
3
3≥0, so absolute value keeps the input and |3|=3.
Reviewed step-by-step derivation
Absolute value · qf-absolute-value-exact-evaluation · candidate
Using the piecewise definition over the real numbers, compute |4| exactly.
4
4≥0, so absolute value keeps the input and |4|=4.
Reviewed step-by-step derivation
Absolute value · qf-absolute-value-exact-evaluation · candidate
Using the piecewise definition over the real numbers, compute |5| exactly.
5
5≥0, so absolute value keeps the input and |5|=5.
Reviewed step-by-step derivation
Absolute value · qf-absolute-value-exact-evaluation · candidate
Using the piecewise definition over the real numbers, compute |6| exactly.
6
6≥0, so absolute value keeps the input and |6|=6.
Reviewed step-by-step derivation
Absolute value · qf-absolute-value-exact-evaluation · candidate
Using the piecewise definition over the real numbers, compute |7| exactly.
7
7≥0, so absolute value keeps the input and |7|=7.
Reviewed step-by-step derivation
Absolute value · qf-absolute-value-exact-evaluation · candidate
Using the piecewise definition over the real numbers, compute |8| exactly.
8
8≥0, so absolute value keeps the input and |8|=8.
Reviewed step-by-step derivation
Absolute value · qf-absolute-value-exact-evaluation · candidate
Using the piecewise definition over the real numbers, compute |9| exactly.
9
9≥0, so absolute value keeps the input and |9|=9.
Reviewed step-by-step derivation
Absolute value · qf-absolute-value-exact-evaluation · candidate
Using the piecewise definition over the real numbers, compute |10| exactly.
10
10≥0, so absolute value keeps the input and |10|=10.
Reviewed step-by-step derivation
Absolute value · qf-absolute-value-exact-evaluation · candidate
Using the piecewise definition over the real numbers, compute |11| exactly.
11
11≥0, so absolute value keeps the input and |11|=11.
Reviewed step-by-step derivation
Absolute value · qf-absolute-value-exact-evaluation · candidate
Using the piecewise definition over the real numbers, compute |12| exactly.
12
12≥0, so absolute value keeps the input and |12|=12.
Reviewed step-by-step derivation
Absolute value · qf-absolute-value-exact-evaluation · candidate
For the real number x=12, which branch of the piecewise definition of |x| applies?
nonnegative branch x
x=12≥0, so use the nonnegative branch x and obtain |x|=12.
Reviewed step-by-step derivation
Absolute value · qf-absolute-value-piecewise-branch · candidate
For the real number x=11, which branch of the piecewise definition of |x| applies?
nonnegative branch x
x=11≥0, so use the nonnegative branch x and obtain |x|=11.
Reviewed step-by-step derivation
Absolute value · qf-absolute-value-piecewise-branch · candidate
For the real number x=10, which branch of the piecewise definition of |x| applies?
nonnegative branch x
x=10≥0, so use the nonnegative branch x and obtain |x|=10.
Reviewed step-by-step derivation
Absolute value · qf-absolute-value-piecewise-branch · candidate
For the real number x=9, which branch of the piecewise definition of |x| applies?
nonnegative branch x
x=9≥0, so use the nonnegative branch x and obtain |x|=9.
Reviewed step-by-step derivation
Absolute value · qf-absolute-value-piecewise-branch · candidate
For the real number x=8, which branch of the piecewise definition of |x| applies?
nonnegative branch x
x=8≥0, so use the nonnegative branch x and obtain |x|=8.
Reviewed step-by-step derivation
Absolute value · qf-absolute-value-piecewise-branch · candidate
For the real number x=7, which branch of the piecewise definition of |x| applies?
nonnegative branch x
x=7≥0, so use the nonnegative branch x and obtain |x|=7.
Reviewed step-by-step derivation
Absolute value · qf-absolute-value-piecewise-branch · candidate
For the real number x=6, which branch of the piecewise definition of |x| applies?
nonnegative branch x
x=6≥0, so use the nonnegative branch x and obtain |x|=6.
Reviewed step-by-step derivation
Absolute value · qf-absolute-value-piecewise-branch · candidate
For the real number x=5, which branch of the piecewise definition of |x| applies?
nonnegative branch x
x=5≥0, so use the nonnegative branch x and obtain |x|=5.
Reviewed step-by-step derivation
Absolute value · qf-absolute-value-piecewise-branch · candidate
For the real number x=4, which branch of the piecewise definition of |x| applies?
nonnegative branch x
x=4≥0, so use the nonnegative branch x and obtain |x|=4.
Reviewed step-by-step derivation
Absolute value · qf-absolute-value-piecewise-branch · candidate
For the real number x=3, which branch of the piecewise definition of |x| applies?
nonnegative branch x
x=3≥0, so use the nonnegative branch x and obtain |x|=3.
Reviewed step-by-step derivation
Absolute value · qf-absolute-value-piecewise-branch · candidate
For the real number x=2, which branch of the piecewise definition of |x| applies?
nonnegative branch x
x=2≥0, so use the nonnegative branch x and obtain |x|=2.
Reviewed step-by-step derivation
Absolute value · qf-absolute-value-piecewise-branch · candidate
For the real number x=1, which branch of the piecewise definition of |x| applies?
nonnegative branch x
x=1≥0, so use the nonnegative branch x and obtain |x|=1.
Reviewed step-by-step derivation
Absolute value · qf-absolute-value-piecewise-branch · candidate
For the real number x=0, which branch of the piecewise definition of |x| applies?
nonnegative branch x
x=0≥0, so use the nonnegative branch x and obtain |x|=0.
Reviewed step-by-step derivation
Absolute value · qf-absolute-value-piecewise-branch · candidate
For the real number x=-1, which branch of the piecewise definition of |x| applies?
negative branch -x
x=-1<0, so use the negative branch -x and obtain |x|=1.
Reviewed step-by-step derivation
Absolute value · qf-absolute-value-piecewise-branch · candidate
For the real number x=-2, which branch of the piecewise definition of |x| applies?
negative branch -x
x=-2<0, so use the negative branch -x and obtain |x|=2.
Reviewed step-by-step derivation
Absolute value · qf-absolute-value-piecewise-branch · candidate
For the real number x=-3, which branch of the piecewise definition of |x| applies?
negative branch -x
x=-3<0, so use the negative branch -x and obtain |x|=3.
Reviewed step-by-step derivation
Absolute value · qf-absolute-value-piecewise-branch · candidate
For the real number x=-4, which branch of the piecewise definition of |x| applies?
negative branch -x
x=-4<0, so use the negative branch -x and obtain |x|=4.
Reviewed step-by-step derivation
Absolute value · qf-absolute-value-piecewise-branch · candidate
For the real number x=-5, which branch of the piecewise definition of |x| applies?
negative branch -x
x=-5<0, so use the negative branch -x and obtain |x|=5.
Reviewed step-by-step derivation
Absolute value · qf-absolute-value-piecewise-branch · candidate
For the real number x=-6, which branch of the piecewise definition of |x| applies?
negative branch -x
x=-6<0, so use the negative branch -x and obtain |x|=6.
Reviewed step-by-step derivation
Absolute value · qf-absolute-value-piecewise-branch · candidate
For the real number x=-7, which branch of the piecewise definition of |x| applies?
negative branch -x
x=-7<0, so use the negative branch -x and obtain |x|=7.
Reviewed step-by-step derivation
Absolute value · qf-absolute-value-piecewise-branch · candidate
For the real number x=-8, which branch of the piecewise definition of |x| applies?
negative branch -x
x=-8<0, so use the negative branch -x and obtain |x|=8.
Reviewed step-by-step derivation
Absolute value · qf-absolute-value-piecewise-branch · candidate
For the real number x=-9, which branch of the piecewise definition of |x| applies?
negative branch -x
x=-9<0, so use the negative branch -x and obtain |x|=9.
Reviewed step-by-step derivation
Absolute value · qf-absolute-value-piecewise-branch · candidate
For the real number x=-10, which branch of the piecewise definition of |x| applies?
negative branch -x
x=-10<0, so use the negative branch -x and obtain |x|=10.
Reviewed step-by-step derivation
Absolute value · qf-absolute-value-piecewise-branch · candidate
For the real number x=-11, which branch of the piecewise definition of |x| applies?
negative branch -x
x=-11<0, so use the negative branch -x and obtain |x|=11.
Reviewed step-by-step derivation
Absolute value · qf-absolute-value-piecewise-branch · candidate
For the real number x=-12, which branch of the piecewise definition of |x| applies?
negative branch -x
x=-12<0, so use the negative branch -x and obtain |x|=12.
Reviewed step-by-step derivation
Absolute value · qf-absolute-value-piecewise-branch · candidate
On the real number line, a=-12 and b=-15. Compute the distance |a-b| exactly.
3
|a-b|=|-12-(-15)|=|3|=3; exchanging the endpoints gives the same distance.
Reviewed step-by-step derivation
Absolute value · qf-absolute-value-distance · candidate
On the real number line, a=-11 and b=-8. Compute the distance |a-b| exactly.
3
|a-b|=|-11-(-8)|=|-3|=3; exchanging the endpoints gives the same distance.
Reviewed step-by-step derivation
Absolute value · qf-absolute-value-distance · candidate
On the real number line, a=-10 and b=-1. Compute the distance |a-b| exactly.
9
|a-b|=|-10-(-1)|=|-9|=9; exchanging the endpoints gives the same distance.
Reviewed step-by-step derivation
Absolute value · qf-absolute-value-distance · candidate
On the real number line, a=-9 and b=6. Compute the distance |a-b| exactly.
15
|a-b|=|-9-(6)|=|-15|=15; exchanging the endpoints gives the same distance.
Reviewed step-by-step derivation
Absolute value · qf-absolute-value-distance · candidate
On the real number line, a=-8 and b=13. Compute the distance |a-b| exactly.
21
|a-b|=|-8-(13)|=|-21|=21; exchanging the endpoints gives the same distance.
Reviewed step-by-step derivation
Absolute value · qf-absolute-value-distance · candidate
On the real number line, a=-7 and b=-11. Compute the distance |a-b| exactly.
4
|a-b|=|-7-(-11)|=|4|=4; exchanging the endpoints gives the same distance.
Reviewed step-by-step derivation
Absolute value · qf-absolute-value-distance · candidate
On the real number line, a=-6 and b=-4. Compute the distance |a-b| exactly.
2
|a-b|=|-6-(-4)|=|-2|=2; exchanging the endpoints gives the same distance.
Reviewed step-by-step derivation
Absolute value · qf-absolute-value-distance · candidate
On the real number line, a=-5 and b=3. Compute the distance |a-b| exactly.
8
|a-b|=|-5-(3)|=|-8|=8; exchanging the endpoints gives the same distance.
Reviewed step-by-step derivation
Absolute value · qf-absolute-value-distance · candidate
On the real number line, a=-4 and b=10. Compute the distance |a-b| exactly.
14
|a-b|=|-4-(10)|=|-14|=14; exchanging the endpoints gives the same distance.
Reviewed step-by-step derivation
Absolute value · qf-absolute-value-distance · candidate
On the real number line, a=-3 and b=-14. Compute the distance |a-b| exactly.
11
|a-b|=|-3-(-14)|=|11|=11; exchanging the endpoints gives the same distance.
Reviewed step-by-step derivation
Absolute value · qf-absolute-value-distance · candidate
On the real number line, a=-2 and b=-7. Compute the distance |a-b| exactly.
5
|a-b|=|-2-(-7)|=|5|=5; exchanging the endpoints gives the same distance.
Reviewed step-by-step derivation
Absolute value · qf-absolute-value-distance · candidate
On the real number line, a=-1 and b=0. Compute the distance |a-b| exactly.
1
|a-b|=|-1-(0)|=|-1|=1; exchanging the endpoints gives the same distance.
Reviewed step-by-step derivation
Absolute value · qf-absolute-value-distance · candidate
On the real number line, a=0 and b=7. Compute the distance |a-b| exactly.
7
|a-b|=|0-(7)|=|-7|=7; exchanging the endpoints gives the same distance.
Reviewed step-by-step derivation
Absolute value · qf-absolute-value-distance · candidate
On the real number line, a=1 and b=14. Compute the distance |a-b| exactly.
13
|a-b|=|1-(14)|=|-13|=13; exchanging the endpoints gives the same distance.
Reviewed step-by-step derivation
Absolute value · qf-absolute-value-distance · candidate
On the real number line, a=2 and b=-10. Compute the distance |a-b| exactly.
12
|a-b|=|2-(-10)|=|12|=12; exchanging the endpoints gives the same distance.
Reviewed step-by-step derivation
Absolute value · qf-absolute-value-distance · candidate
On the real number line, a=3 and b=-3. Compute the distance |a-b| exactly.
6
|a-b|=|3-(-3)|=|6|=6; exchanging the endpoints gives the same distance.
Reviewed step-by-step derivation
Absolute value · qf-absolute-value-distance · candidate
On the real number line, a=4 and b=4. Compute the distance |a-b| exactly.
0
|a-b|=|4-(4)|=|0|=0; exchanging the endpoints gives the same distance.
Reviewed step-by-step derivation
Absolute value · qf-absolute-value-distance · candidate
On the real number line, a=5 and b=11. Compute the distance |a-b| exactly.
6
|a-b|=|5-(11)|=|-6|=6; exchanging the endpoints gives the same distance.
Reviewed step-by-step derivation
Absolute value · qf-absolute-value-distance · candidate
On the real number line, a=6 and b=-13. Compute the distance |a-b| exactly.
19
|a-b|=|6-(-13)|=|19|=19; exchanging the endpoints gives the same distance.
Reviewed step-by-step derivation
Absolute value · qf-absolute-value-distance · candidate
On the real number line, a=7 and b=-6. Compute the distance |a-b| exactly.
13
|a-b|=|7-(-6)|=|13|=13; exchanging the endpoints gives the same distance.
Reviewed step-by-step derivation
Absolute value · qf-absolute-value-distance · candidate
On the real number line, a=8 and b=1. Compute the distance |a-b| exactly.
7
|a-b|=|8-(1)|=|7|=7; exchanging the endpoints gives the same distance.
Reviewed step-by-step derivation
Absolute value · qf-absolute-value-distance · candidate
On the real number line, a=9 and b=8. Compute the distance |a-b| exactly.
1
|a-b|=|9-(8)|=|1|=1; exchanging the endpoints gives the same distance.
Reviewed step-by-step derivation
Absolute value · qf-absolute-value-distance · candidate
On the real number line, a=10 and b=15. Compute the distance |a-b| exactly.
5
|a-b|=|10-(15)|=|-5|=5; exchanging the endpoints gives the same distance.
Reviewed step-by-step derivation
Absolute value · qf-absolute-value-distance · candidate
On the real number line, a=11 and b=-9. Compute the distance |a-b| exactly.
20
|a-b|=|11-(-9)|=|20|=20; exchanging the endpoints gives the same distance.
Reviewed step-by-step derivation
Absolute value · qf-absolute-value-distance · candidate
On the real number line, a=12 and b=-2. Compute the distance |a-b| exactly.
14
|a-b|=|12-(-2)|=|14|=14; exchanging the endpoints gives the same distance.
Reviewed step-by-step derivation
Absolute value · qf-absolute-value-distance · candidate
Over the real numbers, classify the solution set of |x|=-4.
no solution
Absolute value is nonnegative and cannot equal -4, so there is no solution.
Reviewed step-by-step derivation
Absolute value · qf-absolute-value-equation-class · candidate
Over the real numbers, classify the solution set of |x|=-3.
no solution
Absolute value is nonnegative and cannot equal -3, so there is no solution.
Reviewed step-by-step derivation
Absolute value · qf-absolute-value-equation-class · candidate
Over the real numbers, classify the solution set of |x|=-2.
no solution
Absolute value is nonnegative and cannot equal -2, so there is no solution.
Reviewed step-by-step derivation
Absolute value · qf-absolute-value-equation-class · candidate
Over the real numbers, classify the solution set of |x|=-1.
no solution
Absolute value is nonnegative and cannot equal -1, so there is no solution.
Reviewed step-by-step derivation
Absolute value · qf-absolute-value-equation-class · candidate
Over the real numbers, classify the solution set of |x|=0.
unique solution x=0
|x|=0 holds exactly at x=0.
Reviewed step-by-step derivation
Absolute value · qf-absolute-value-equation-class · candidate
Over the real numbers, classify the solution set of |x|=1.
two solutions x=-1, 1
The real numbers at distance 1 from 0 are x=-1 and x=1.
Reviewed step-by-step derivation
Absolute value · qf-absolute-value-equation-class · candidate
Over the real numbers, classify the solution set of |x|=2.
two solutions x=-2, 2
The real numbers at distance 2 from 0 are x=-2 and x=2.
Reviewed step-by-step derivation
Absolute value · qf-absolute-value-equation-class · candidate
Over the real numbers, classify the solution set of |x|=3.
two solutions x=-3, 3
The real numbers at distance 3 from 0 are x=-3 and x=3.
Reviewed step-by-step derivation
Absolute value · qf-absolute-value-equation-class · candidate
Over the real numbers, classify the solution set of |x|=4.
two solutions x=-4, 4
The real numbers at distance 4 from 0 are x=-4 and x=4.
Reviewed step-by-step derivation
Absolute value · qf-absolute-value-equation-class · candidate
Over the real numbers, classify the solution set of |x|=5.
two solutions x=-5, 5
The real numbers at distance 5 from 0 are x=-5 and x=5.
Reviewed step-by-step derivation
Absolute value · qf-absolute-value-equation-class · candidate
Over the real numbers, classify the solution set of |x|=6.
two solutions x=-6, 6
The real numbers at distance 6 from 0 are x=-6 and x=6.
Reviewed step-by-step derivation
Absolute value · qf-absolute-value-equation-class · candidate
Over the real numbers, classify the solution set of |x|=7.
two solutions x=-7, 7
The real numbers at distance 7 from 0 are x=-7 and x=7.
Reviewed step-by-step derivation
Absolute value · qf-absolute-value-equation-class · candidate
Over the real numbers, classify the solution set of |x|=8.
two solutions x=-8, 8
The real numbers at distance 8 from 0 are x=-8 and x=8.
Reviewed step-by-step derivation
Absolute value · qf-absolute-value-equation-class · candidate
Over the real numbers, classify the solution set of |x|=9.
two solutions x=-9, 9
The real numbers at distance 9 from 0 are x=-9 and x=9.
Reviewed step-by-step derivation
Absolute value · qf-absolute-value-equation-class · candidate
Over the real numbers, classify the solution set of |x|=10.
two solutions x=-10, 10
The real numbers at distance 10 from 0 are x=-10 and x=10.
Reviewed step-by-step derivation
Absolute value · qf-absolute-value-equation-class · candidate
Over the real numbers, classify the solution set of |x|=11.
two solutions x=-11, 11
The real numbers at distance 11 from 0 are x=-11 and x=11.
Reviewed step-by-step derivation
Absolute value · qf-absolute-value-equation-class · candidate
Over the real numbers, classify the solution set of |x|=12.
two solutions x=-12, 12
The real numbers at distance 12 from 0 are x=-12 and x=12.
Reviewed step-by-step derivation
Absolute value · qf-absolute-value-equation-class · candidate
Over the real numbers, classify the solution set of |x|=13.
two solutions x=-13, 13
The real numbers at distance 13 from 0 are x=-13 and x=13.
Reviewed step-by-step derivation
Absolute value · qf-absolute-value-equation-class · candidate
Over the real numbers, classify the solution set of |x|=14.
two solutions x=-14, 14
The real numbers at distance 14 from 0 are x=-14 and x=14.
Reviewed step-by-step derivation
Absolute value · qf-absolute-value-equation-class · candidate
Over the real numbers, classify the solution set of |x|=15.
two solutions x=-15, 15
The real numbers at distance 15 from 0 are x=-15 and x=15.
Reviewed step-by-step derivation
Absolute value · qf-absolute-value-equation-class · candidate
Over the real numbers, classify the solution set of |x|=16.
two solutions x=-16, 16
The real numbers at distance 16 from 0 are x=-16 and x=16.
Reviewed step-by-step derivation
Absolute value · qf-absolute-value-equation-class · candidate
Over the real numbers, classify the solution set of |x|=17.
two solutions x=-17, 17
The real numbers at distance 17 from 0 are x=-17 and x=17.
Reviewed step-by-step derivation
Absolute value · qf-absolute-value-equation-class · candidate
Over the real numbers, classify the solution set of |x|=18.
two solutions x=-18, 18
The real numbers at distance 18 from 0 are x=-18 and x=18.
Reviewed step-by-step derivation
Absolute value · qf-absolute-value-equation-class · candidate
Over the real numbers, classify the solution set of |x|=19.
two solutions x=-19, 19
The real numbers at distance 19 from 0 are x=-19 and x=19.
Reviewed step-by-step derivation
Absolute value · qf-absolute-value-equation-class · candidate
Over the real numbers, classify the solution set of |x|=20.
two solutions x=-20, 20
The real numbers at distance 20 from 0 are x=-20 and x=20.
Reviewed step-by-step derivation
Absolute value · qf-absolute-value-equation-class · candidate
Canonical question JSONL · English JSONL · Validation report