Question

if fg = 7x, gh = x + 1, and fh = 9, what is fg?
diagram: points f, g, h on a line segment with fg labeled ( 7x ), gh labeled ( x + 1 ), and fh labeled ( 9 )
simplify your answer and write it as a proper fraction, mixed number, or integer

Explanation:

Step1: Set up the equation

From the segment addition postulate, we know that \( FG + GH = FH \). Substituting the given expressions, we get \( 7x+(x + 1)=9 \).

Step2: Simplify the left side

Combine like terms: \( 7x+x+1 = 8x + 1 \), so the equation becomes \( 8x+1=9 \).

Step3: Solve for x

Subtract 1 from both sides: \( 8x=9 - 1=8 \). Then divide both sides by 8: \( x=\frac{8}{8}=1 \).

Step4: Find FG

Since \( FG = 7x \) and \( x = 1 \), substitute \( x \) into the expression for \( FG \): \( FG=7\times1 = 7 \).

Answer:

7