Question

1. solve for x. 10x + 44 8x - 23

Explanation:

Step1: Apply the mid - segment theorem

The mid - segment of a triangle is parallel to the third side and half its length. So, \(10x + 44=2(8x - 23)\).

Step2: Expand the right - hand side

Expand \(2(8x - 23)\) to get \(16x-46\). The equation becomes \(10x + 44=16x-46\).

Step3: Move the \(x\) terms to one side and constants to the other

Subtract \(10x\) from both sides: \(44 = 6x-46\). Then add \(46\) to both sides: \(44 + 46=6x\), so \(90 = 6x\).

Step4: Solve for \(x\)

Divide both sides by \(6\): \(x=\frac{90}{6}\).

Answer:

\(x = 15\)