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.
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