Question

select the correct equation and correct answer to solve for x using the triangle below. mark all correct answers a. 2(2x - 15)=2x - 8 b. 2x - 15 = 2x - 8 c. 2(2x - 8)=2x - 15 d. 0.5 e. 11 f. 6

Explanation:

Step1: Apply mid - segment theorem

In a triangle, the mid - segment (the line segment connecting the mid - points of two sides) is half the length of the third side. Here, the line segment $LK$ is a mid - segment of $\triangle QRP$. So, $2(2x - 15)=2x - 8$.

Step2: Solve the equation

First, expand the left - hand side: $4x-30 = 2x - 8$.
Then, subtract $2x$ from both sides: $4x-2x-30=2x - 2x - 8$, which simplifies to $2x-30=-8$.
Next, add 30 to both sides: $2x-30 + 30=-8 + 30$, giving $2x = 22$.
Finally, divide both sides by 2: $x = 11$.

Answer:

a. $2(2x - 15)=2x - 8$
e. 11