Question

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

diagram: points c, d, e on a line segment; cd is labeled ( x + 3 ), de is labeled ( 8x - 9 )

Explanation:

Step1: Determine CE length

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

Step2: Set up equation

We know \( CE = 7x + 4 \) and \( CE = 9x - 6 \). So \( 9x - 6=7x + 4 \).

Step3: Solve for x

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

Answer:

\( x = 5 \)