Question

if fg = 5x + 2, gh = 6x + 13, and fh = 14x - 9, what is fh? simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Use segment - addition postulate

Since $FH=FG + GH$, we have the equation $(5x + 2)+(6x + 13)=14x-9$.

Step2: Combine like - terms on the left - hand side

$5x+6x + 2+13=14x-9$, which simplifies to $11x + 15=14x-9$.

Step3: Isolate the variable terms

Subtract $11x$ from both sides: $11x+15-11x=14x - 9-11x$, getting $15 = 3x-9$.

Step4: Solve for $x$

Add 9 to both sides: $15 + 9=3x-9 + 9$, so $24 = 3x$. Then divide both sides by 3: $\frac{24}{3}=x$, and $x = 8$.

Step5: Find the value of $FH$

Substitute $x = 8$ into the expression for $FH$: $FH=14x-9=14\times8-9$.
$FH=112 - 9=103$.

Answer:

$103$