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 b.

Explanation:

Step1: Form the equation

The black line length is \(4b + b=5b\) (combining like terms for black line: \(4b\) and \(b\)). The blue line length is \(7\). The green line length is \(13\). So the equation is \(5b - 7=13\).

Step2: Solve for \(b\)

Add \(7\) to both sides: \(5b-7 + 7=13 + 7\) which simplifies to \(5b = 20\).
Divide both sides by \(5\): \(\frac{5b}{5}=\frac{20}{5}\), so \(b = 4\).

Answer:

The equation is \(5b - 7 = 13\) and \(b = 4\)