Question

1. if df = 9x - 39, find the value of ef.

Explanation:

Step1: Set up equation

Since $DF=DE + EF$, we have $9x - 39=47+(3x + 10)$.

Step2: Simplify right - hand side

$9x - 39=47 + 3x+10$, so $9x - 39=3x + 57$.

Step3: Move x terms to one side

Subtract $3x$ from both sides: $9x-3x - 39=3x-3x + 57$, which gives $6x-39 = 57$.

Step4: Isolate x

Add 39 to both sides: $6x-39 + 39=57 + 39$, so $6x=96$.

Step5: Solve for x

Divide both sides by 6: $x=\frac{96}{6}=16$.

Step6: Find EF

Substitute $x = 16$ into the expression for $EF$: $EF=3x + 10=3\times16+10=48 + 10=52$.

Answer:

$EF = 52$