Question

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

Explanation:

Step1: Set up the equation

The length of the black line is the sum of \( r \), \( 3r \), and \( 11 \), and it equals the length of the green line, which is \( 47 \). So the equation is \( r + 3r + 11 = 47 \).

Step2: Combine like terms

Combine \( r \) and \( 3r \) to get \( 4r \). So the equation becomes \( 4r + 11 = 47 \).

Step3: Subtract 11 from both sides

Subtract \( 11 \) from both sides of the equation: \( 4r + 11 - 11 = 47 - 11 \), which simplifies to \( 4r = 36 \).

Step4: Divide by 4

Divide both sides by \( 4 \): \( \frac{4r}{4} = \frac{36}{4} \), so \( r = 9 \).

Answer:

Equation: \( r + 3r + 11 = 47 \) (or simplified to \( 4r + 11 = 47 \))
\( r = 9 \)