Question

point f is on line segment $overline{eg}$. given $fg = 8$, $ef = 2x + 4$, and $eg = 4x - 10$, determine the numerical length of $overline{ef}$.

Explanation:

Step1: Use segment - addition postulate

Since point F is on line segment $\overline{EG}$, we have $EF + FG=EG$. Substitute the given expressions: $(2x + 4)+8=4x-10$.

Step2: Simplify the left - hand side of the equation

Combine like terms: $2x+12 = 4x-10$.

Step3: Isolate the variable terms

Subtract $2x$ from both sides: $12=4x - 2x-10$, which simplifies to $12 = 2x-10$.

Step4: Solve for x

Add 10 to both sides: $12 + 10=2x$, so $22 = 2x$. Then divide both sides by 2: $x = 11$.

Step5: Find the length of EF

Substitute $x = 11$ into the expression for $EF$: $EF=2x + 4=2\times11+4=22 + 4=26$.

Answer:

26