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 ( q ).
the green line is labeled 49. the black line is divided into segments: ( q ), ( q ), ( 5q ), and 7.
equation:
( q = )

Explanation:

Part 1: Writing the Equation

Step1: Find length of black line

The black line is composed of \( q \), \( q \), \( 5q \), and \( 7 \). So sum these terms: \( q + q + 5q + 7 \).

Step2: Combine like terms

Combine the \( q \)-terms: \( q + q + 5q = (1 + 1 + 5)q = 7q \). So the length of the black line is \( 7q + 7 \).

Step3: Set equal to green line

The green line has length \( 49 \), so the equation is \( 7q + 7 = 49 \).

Part 2: Solving for \( q \)

Step1: Subtract 7 from both sides

To isolate the term with \( q \), subtract 7 from both sides: \( 7q + 7 - 7 = 49 - 7 \), which simplifies to \( 7q = 42 \).

Step2: Divide by 7

Divide both sides by 7: \( \frac{7q}{7} = \frac{42}{7} \), so \( q = 6 \).

Answer:

(Equation):
\( 7q + 7 = 49 \)