Question

if ef = 11x - 19, fg = 2, and eg = 4x - 3, what is eg? simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Use segment - addition postulate

Since $EG = EF+FG$, we have the equation $4x - 3=(11x - 19)+2$.

Step2: Simplify the right - hand side of the equation

$(11x - 19)+2=11x-17$, so the equation becomes $4x - 3 = 11x-17$.

Step3: Isolate the variable terms

Subtract $4x$ from both sides: $4x-4x - 3=11x-4x - 17$, which simplifies to $- 3 = 7x-17$.

Step4: Solve for $x$

Add 17 to both sides: $-3 + 17=7x-17 + 17$, getting $14 = 7x$. Then divide both sides by 7: $\frac{14}{7}=x$, so $x = 2$.

Step5: Find the value of $EG$

Substitute $x = 2$ into the expression for $EG$. Since $EG=4x - 3$, then $EG=4\times2-3$.
$EG=8 - 3=5$.

Answer:

5