Question

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

• A. None
• B. Two
• C. Nine
• D. Fourteen
• E. Infinitely many

Answer 1

The correct option is C Nine

Given, $|2x+6|<\frac{19}{2}$

We have two possible inequalities they are

$2x+6<\frac{19}{2}$ and $2x+6>-\frac{19}{2}$
$\Rightarrow x<\frac{7}{4}$ and $x>-\frac{31}{4}$
The number of integers between $x$ consists of the integers between $-7.75$ and $1.75$.
Thus, $9$ integers are there.