find the value of x. x = ?

Explanation:

Step1: Use similar - triangle property

Since the two triangles are similar, the ratios of their corresponding sides are equal. We have the proportion $\frac{14}{10}=\frac{2x - 3}{x}$.

Step2: Cross - multiply

Cross - multiplying the proportion gives us $14x=10(2x - 3)$.

Step3: Expand the right - hand side

Expand $10(2x - 3)$ to get $14x = 20x-30$.

Step4: Move the x terms to one side

Subtract $20x$ from both sides: $14x-20x=-30$, which simplifies to $-6x=-30$.

Step5: Solve for x

Divide both sides by $-6$: $x = 5$.

Answer:

$5$