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 ?