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 m. 21 2m 2m 2m m equation: m =

Explanation:

Part 1: Writing the Equation

Step1: Find length of black line

The black line has segments \(2m\), \(2m\), \(2m\), and \(m\). Sum them: \(2m + 2m + 2m + m\).

Step2: Set equal to green line

Green line length is \(21\), so equation: \(2m + 2m + 2m + m = 21\).

Step3: Combine like terms

Combine \(2m + 2m + 2m + m\): \( (2 + 2 + 2 + 1)m = 7m\). So equation is \(7m = 21\).

Equation: \(7m = 21\)

Part 2: Solving for \(m\)

Step1: Isolate \(m\)

Divide both sides of \(7m = 21\) by \(7\): \(\frac{7m}{7} = \frac{21}{7}\).

Step2: Simplify

Simplify to get \(m = 3\).

Answer:

Equation: \(7m = 21\)
\(m = 3\)