Question

1. write an equation that says that the length of the green line is equal to the length of the black line. combine like terms.
2. then solve for u.

green line length: 46
black line segments: u, u, 12
equation:
u =

Explanation:

Part 1: Writing the Equation

Step1: Analyze the black line length

The black line is composed of two segments of length \( u \) and one segment of length 12. So its total length is \( u + u + 12 \).

Step2: Set equal to green line length

The green line has length 46. So the equation is \( u + u + 12 = 46 \).

Step3: Combine like terms

Combine the \( u \) terms: \( 2u + 12 = 46 \).

Step1: Subtract 12 from both sides

Subtract 12 from each side to isolate the term with \( u \): \( 2u + 12 - 12 = 46 - 12 \)
Simplify: \( 2u = 34 \)

Step2: Divide by 2

Divide both sides by 2 to solve for \( u \): \( \frac{2u}{2} = \frac{34}{2} \)
Simplify: \( u = 17 \)

Answer:

Equation: \( 2u + 12 = 46 \)

Part 2: Solving for \( u \)