Question

How many integers are there in the solution set of $|2x+6|<\frac{19}{2}?$

• A. One
• B. Two
• C. Fourteen
• D. Nine

Answer 1

The correct option is D Nine

Simplifying, we get
$\frac{-19}{2}<2x+6<\frac{19}{2}$
Hence
$-19<4x+12<19$
$-31<4x<7$
$\frac{-31}{4}<x<\frac{7}{4}$
$-7.75<x<1.75$
Hence the integers in the above solution set are
$\{-7,-6,-5,-4,-3,-2,-1,0,1\}$
Hence in total 9 integers.