Carcass wrote:

How many integers \(x\) satisfy \(|2x + 3 | < 6\)

A. 1

B. 2

C. 6

D. 7

E. 8

As we are dealing with modulus we have to consider both negative and positive aspects.

Case 1 : when 2x + 3 is positive.

2x + 3 < 6

x < 1.5.

Case 2: when 2x + 3 is negative .

-2x -3 < 6

x > -4.5.

So,

-4.5 <x<1.5.

There are 6 values in total : -4, -3 , -2, -1, 0 , 1.

The best answer is C.