Question

write an equation that says that the length of the green line is equal to the length of the black line minus the length of the blue line. combine like terms. then solve for u. equation: u =

Explanation:

Step1: Analyze the line lengths

The black line is length 23, the blue line is composed of two segments each of length \( u \), so total blue length is \( u + u = 2u \). The green line is length 7. The equation is \( 7 = 23 - 2u \) (or \( 2u + 7 = 23 \), equivalent).

Step2: Solve the equation \( 2u + 7 = 23 \)

Subtract 7 from both sides: \( 2u + 7 - 7 = 23 - 7 \)
Simplify: \( 2u = 16 \)
Divide both sides by 2: \( \frac{2u}{2} = \frac{16}{2} \)
Simplify: \( u = 8 \)

Answer:

Equation: \( 2u + 7 = 23 \) (or \( 7 = 23 - 2u \))
\( u = 8 \)