ACT · Elementary Algebra · Absolute value equations and inequalities
Question act-q-00328
Hard Multiple choice No calculator
The question
What is the sum of all values of x that satisfy |x − 2| = 8?
- 10
- 8
- 2
- 4
Show answer & worked solution
Answer: 4
Worked solution. |x − 2| = 8 splits into x − 2 = 8 (so x = 10) and x − 2 = −8 (so x = -6). Sum = 10 + -6 = 4.
Why each wrong choice is wrong. Solving for only one of the two cases is the most common error, giving you just one root. The trap distractor offers exactly that.
Test-day tactic. Every absolute-value equation splits into two cases. Solve both, then answer the specific question — sometimes it asks for the sum, sometimes a single value.
About this question type
Items test the absolute-value definition: |x| = k splits into x = k and x = −k; |x| < k splits into −k < x < k; |x| > k splits into x > k or x < −k.
You will see a question shaped like this one on roughly every other official ACT form, typically at the back end of the section, where the score gradient is steepest. Treat any miss in this subtopic as a signal to drill the subtopic page before you do another full practice test.
Continue practising
← Previous question · Next question →
Back to all Absolute value equations and inequalities questions