Question

In the diagram, A||B and B||C . Find the values of X

Answer 1

keeping in mind that an absolute value expression is really a duet in disguise, namely there's positive and negative version of it, Check the picture below.

`\pm (3x+12)~~ = ~~105 \\\\[-0.35em] ~\dotfill\\\\ +(3x+12)~~ = ~~105\implies 3x=93\implies x=\cfrac{93}{3}\implies \boxed{x=31} \\\\[-0.35em] ~\dotfill\\\\ -(3x+12)~~ = ~~105\implies 3x+12=-105\implies 3x=-117 \\\\\\ x=\cfrac{-117}{3}\implies \boxed{x=-39}`