Question

if ef = x + 8, fg = 19, and eg = 10x - 18, what is ef? 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 substitute the given expressions: $10x-18=(x + 8)+19$.

Step2: Simplify the right - hand side

$(x + 8)+19=x+8 + 19=x + 27$. So the equation becomes $10x-18=x + 27$.

Step3: Isolate the variable terms

Subtract $x$ from both sides: $10x-x-18=x-x + 27$, which simplifies to $9x-18=27$.

Step4: Isolate the variable

Add 18 to both sides: $9x-18 + 18=27+18$, so $9x=45$.

Step5: Solve for $x$

Divide both sides by 9: $\frac{9x}{9}=\frac{45}{9}$, and $x = 5$.

Step6: Find $EF$

Substitute $x = 5$ into the expression for $EF$: $EF=x + 8=5 + 8=13$.

Answer:

13