Question

if fg = 13x - 6, gh = 7x + 12, and fh = 19x + 16, 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 substitute the given expressions: $19x + 16=(13x - 6)+(7x + 12)$.

Step2: Simplify the right - hand side

Combine like terms on the right - hand side: $(13x - 6)+(7x + 12)=13x+7x - 6 + 12=20x+6$. So, $19x + 16=20x+6$.

Step3: Solve for x

Subtract $19x$ from both sides: $19x+16-19x=20x + 6-19x$, which gives $16=x + 6$. Then subtract 6 from both sides: $x=16 - 6=10$.

Step4: Find the value of FH

Substitute $x = 10$ into the expression for $FH$. Since $FH=19x + 16$, then $FH=19\times10+16=190+16=206$.

Answer:

$206$