Question

|4x - 5| = 8A. x= 13/4 or x= -3/4B. x= 3/4 or x= -13/4C. x= 13/4 onlyD. no solutionE. infinitely many solutions

Answer 1

We will solve this problem thus:

$\begin{gathered} \lvert4x-5\rvert=8 \\ \text{means} \\ 4x-5=+8\text{ or 4x-5= -8} \end{gathered}$

Solving further we will have:

$\begin{gathered} 4x=8+5\text{ or 4x=-8}+5 \\ 4x=13\text{ or 4x = -3} \\ x=\frac{13}{4}\text{ or x=}\frac{-3}{4} \\ \text{The correct answer is option A} \end{gathered}$