Question

find the value of x.
50
30
9x
5x+2
x = ?

Explanation:

Step1: Set up proportion (similar triangles)

$\frac{9x}{5x+2}=\frac{50}{30}$

Step2: Simplify the right-hand fraction

$\frac{9x}{5x+2}=\frac{5}{3}$

Step3: Cross-multiply to eliminate fractions

$3\times9x = 5\times(5x+2)$
$27x = 25x + 10$

Step4: Isolate x term

$27x - 25x = 10$
$2x = 10$

Step5: Solve for x

$x = \frac{10}{2}=2$

Answer:

$x = 2$