Question

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

Explanation:

Step1: Apply the mid - segment theorem

The mid - segment of a triangle is half the length of the base. So, \(8x - 23=\frac{1}{2}(10x + 44)\).

Step2: Multiply both sides by 2

Multiply both sides of the equation \(8x - 23=\frac{1}{2}(10x + 44)\) by 2 to get \(2(8x - 23)=10x + 44\).
Using the distributive property \(a(b + c)=ab+ac\), we have \(16x-46 = 10x + 44\).

Step3: Subtract \(10x\) from both sides

\(16x-10x-46=10x - 10x+44\), which simplifies to \(6x-46 = 44\).

Step4: Add 46 to both sides

\(6x-46 + 46=44 + 46\), so \(6x=90\).

Step5: Divide both sides by 6

\(x=\frac{90}{6}\).

Answer:

\(x = 15\)