Question

$\triangle cat \cong \triangle dog$. find x.

Explanation:

Step1: Equate congruent sides

Since $\triangle CAT \cong \triangle DOG$, corresponding sides $\overline{AC}$ and $\overline{OD}$ are equal:
$8x - 6 = 3x + 9$

Step2: Isolate x terms

Subtract $3x$ from both sides:
$8x - 3x - 6 = 9$
$5x - 6 = 9$

Step3: Solve for x

Add 6 to both sides, then divide by 5:
$5x = 9 + 6$
$5x = 15$
$x = \frac{15}{5}$

Answer:

$3$