Question

1. solve for x.

h •———4———•g———x-3———•f
←———-9 + 2x———→
x=□

Explanation:

Step1: Set up the equation

From the line segment, we know that \( HF = HG + GF \). So, \( -9 + 2x = 4 + (x - 3) \).

Step2: Simplify the right side

Simplify \( 4+(x - 3) \) to get \( x + 1 \). So the equation becomes \( -9 + 2x = x + 1 \).

Step3: Solve for x

Subtract \( x \) from both sides: \( -9 + 2x - x = x + 1 - x \), which simplifies to \( -9 + x = 1 \). Then add 9 to both sides: \( -9 + x + 9 = 1 + 9 \), so \( x = 10 \).

Answer:

\( x = 10 \)