16Hit1600
Advanced MathVery hardSum of solutions of an absolute-value equality

Advanced Math practice question

The equation |2x − 5| = |x + 1| has two solutions. What is their sum?

Answer: 22/3 or 7.33 or 7.333

Either 2x − 5 = x + 1, giving x = 6, or 2x − 5 = −(x + 1), giving x = 4/3. The sum is 6 + 4/3 = 22/3.

Common wrong answers

If you answered 4
4 comes from 2x − 5 = −x + 1 with a slip, giving x = 2, plus a wrong second root.
If you answered 6
6 is one solution alone.
If you answered 14/3
14/3 subtracts the roots instead of adding.

More Advanced Math questions

Not affiliated with the College Board. SAT is a trademark of the College Board.