Question

find the value of x.
x = (simplify your answer.)

Explanation:

Step1: Apply the midsegment theorem

The midsegment of a triangle is parallel to the third side and half its length. Here, \(6x - 8\) is the midsegment and \(8x + 4\) is the third side. So, \(6x-8=\frac{1}{2}(8x + 4)\).

Step2: Solve the equation

Multiply both sides by 2 to get \(2(6x - 8)=8x + 4\).
Expand: \(12x-16 = 8x+4\).
Subtract \(8x\) from both sides: \(12x-8x-16=8x - 8x+4\), which gives \(4x-16 = 4\).
Add 16 to both sides: \(4x-16 + 16=4 + 16\), so \(4x=20\).
Divide both sides by 4: \(x=\frac{20}{4}\).

Answer:

\(x = 5\)