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PCAT Quantitative Reasoning – Absolute Value Inequality
- by
- Apr 19, 2018
- PCAT Question of the Day
Evaluate |4 – 3a|> 2a + 6.
A. a < –2
B. a > 10
C. –2 < a < 10
D. a < –2 or a > 10
Click for Explanation
D is correct. To solve an expression that includes an absolute value, we must solve for the outcome where the value inside the absolute signs is positive, and for the outcome where the value inside the absolute signs is negative:
| a – 3 | > 2a + 6
4 – 3a > 2a +6 – (4 – 3a) > 2a + 6
-a > 2 -4 + 3a > 2a + 6
a < -2 or a > 10
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