Linear inequality SAT question (medium to difficult)

Question

If (-3*|4x-3| - 3) < 6, what is the range of values for ‘x’?

A) 1/4 < x < 5/4

B) x < 1/4 or x > 5/4

C) −∞ < x < ∞

D) No real numbers

Answer 1

The inequality -3*|4x-3| - 3 < 6 can be rearranged as: -3*|4x-3| < 3+6 =9 ⇒ - |4x-3| < 9/3.

now if we multiply both sides by -1, the inequality reverses into: -3 < |4x-3|. But since for all real values of x, the value of |4x-3| is always greater or equal to 0, then we have a trivial case where all real x values satisfy. Therefore C) −∞ < x < ∞ is the answer.