Question

1. if ce = 7x + 4, find the value of x.

image: line segment with points c, d, e; segment cd labeled ( x + 3 ), segment de labeled ( 8x - 9 )

Explanation:

Step1: Determine CE length formula

From the line segment, \( CE = CD + DE \). So \( CE=(x + 3)+(8x - 9) \). Simplify: \( CE = 9x - 6 \).

Step2: Set up equation

Given \( CE = 7x + 4 \), so \( 9x - 6 = 7x + 4 \).

Step3: Solve for x

Subtract \( 7x \) from both sides: \( 9x - 7x - 6 = 4 \) → \( 2x - 6 = 4 \). Add 6 to both sides: \( 2x = 4 + 6 \) → \( 2x = 10 \). Divide by 2: \( x=\frac{10}{2}=5 \).

Answer:

\( x = 5 \)