Question

16 find the value of x. set up the proportion: x =

Explanation:

Step1: Apply the triangle - proportionality theorem

If a line is parallel to one side of a triangle and intersects the other two sides, then it divides those sides proportionally. So, we set up the proportion $\frac{2x - 3}{x + 2}=\frac{10}{15}$.

Step2: Cross - multiply

Cross - multiplying gives us $15(2x - 3)=10(x + 2)$.
Expanding both sides: $30x-45 = 10x+20$.

Step3: Solve for x

Subtract $10x$ from both sides: $30x-10x-45=10x - 10x+20$, which simplifies to $20x-45 = 20$.
Add 45 to both sides: $20x-45 + 45=20 + 45$, so $20x=65$.
Divide both sides by 20: $x=\frac{65}{20}=\frac{13}{4}=3.25$.

Answer:

Set up the proportion: $\frac{2x - 3}{x + 2}=\frac{10}{15}$
$x = 3.25$