Answer to Question #272187 in Algebra for Mimi

Question

Using the definition of absolute value, evaluate $\begin{vmatrix} X-2/3 =3/4 \end{vmatrix}\mid$

Answer 1

$|x-\frac{2}{3}|=\frac{3}{4}\\ \text{By using definition of absolute value, we have}\\ \implies x-\frac{2}{3}=\frac{3}{4} \space or\space -(x-\frac{2}{3})=\frac{3}{4} \\ \implies x=\frac{2}{3}+\frac{3}{4} \space or \space x= -\frac{3}{4}+\frac{2}{3}\\ \implies x=\frac{17}{12} \space or \space x= -\frac{1}{12}\\$