Question

1. solve for x.

Explanation:

Step1: Use the mid - segment theorem

In a triangle, the mid - segment (a segment connecting the midpoints of two sides of a triangle) is parallel to the third side and its length is half of the length of the third side. Here, \(SR\) is the mid - segment of \(\triangle EFD\), so \(2x - 14=\frac{1}{2}(x + 2)\)

Step2: Solve the equation

Multiply both sides of the equation \(2x - 14=\frac{1}{2}(x + 2)\) by \(2\) to get rid of the fraction:
\(2(2x - 14)=x + 2\)
Expand the left - hand side: \(4x-28=x + 2\)
Subtract \(x\) from both sides: \(4x-x-28=x - x+ 2\), which simplifies to \(3x-28 = 2\)
Add \(28\) to both sides: \(3x-28 + 28=2 + 28\), so \(3x=30\)
Divide both sides by \(3\): \(x=\frac{30}{3}\)

Answer:

\(x = 10\)