Question

if de = 7x + 3 and ef = 9x - 19, what is ef?

Explanation:

Step1: Set DE equal to EF

Since DE = EF (from the equal - length markings on the line segment), we set up the equation $7x + 3=9x - 19$.

Step2: Solve for x

Subtract $7x$ from both sides: $7x+3 - 7x=9x - 19-7x$, which simplifies to $3 = 2x-19$. Then add 19 to both sides: $3 + 19=2x-19 + 19$, giving $22 = 2x$. Divide both sides by 2: $\frac{22}{2}=\frac{2x}{2}$, so $x = 11$.

Step3: Find the length of EF

Substitute $x = 11$ into the expression for EF. EF=$9x - 19$. So EF=$9\times11-19$. First, calculate $9\times11 = 99$. Then $99-19=80$.

Answer:

80