Question

find the value of x.
$x=\boldsymbol{\square}$
in the triangle: $ab=bc$, $bd\perp ac$, $ad=3x+8$, $cd=5x-6$

Explanation:

Step1: Set segments equal (perpendicular bisector)

$3x + 8 = 5x - 6$

Step2: Rearrange to isolate x terms

$8 + 6 = 5x - 3x$

Step3: Simplify and solve for x

$14 = 2x \implies x = \frac{14}{2}$

Answer:

$7$