Question

Segment XZ is bisected by point Y. If XY= 12x, and the measure of XZ= 18x-6, solve for x.​

Answer 1

let's bear in mind that Y is a bisecting point, so it's really cutting XZ into two equal halves.

$\bf \underset{\textit{\Large 18x-6}}{\boxed{X}\stackrel{12x}{\rule[0.35em]{14em}{0.25pt}} Y\stackrel{12x}{\rule[0.35em]{14em}{0.25pt}}\boxed{Z}} \\\\\\ 12x+12x = 18x-6\implies 24x=18x-6 \\\\\\ 6x=-6\implies x=\cfrac{-6}{6}\implies x=-1$

Answer 2

Since XZ is bisected by Y and XY = 12x, that makes YZ equal to 12x

To set it up, 24x = 18x-6

Subtract 18, 6x=-6

Divide by 6 on both sides, x = -1