Bunuel wrote:

If x is an integer and \(|2x+3|≤12\), then which of the following must be true?

A. x < -9

B. x < -8

C. x > -8

D. x < 4

E. x > 4

\(|2x+3|≤12\)

i.e. \(-12 ≤ 2x+3 ≤ 12\)

i.e. \(-12-3 ≤ 2x ≤ 12-3\)

i.e. \(-15 ≤ 2x ≤ 9\)

i.e. \(-7.5 ≤ x ≤ 4.5\)

Out of all options we see

A. x < -9 Is INCORRECT as all values of x are greater than -9

B. x < -8 Is INCORRECT as all values of x are greater than -8

C. x > -8 Is CORRECT because all values of x in the calculated range of values of x are greater than -8D. x < 4 Is INCORRECT because x may be 4 which is NOT less than 4

E. x > 4 Is INCORRECT as x may be less than 4 as well

Answer: Option C

I got the same range but won't x > -8 include values above 4.5 ?