Question

segment addition / subtraction (algebra)
score: 1/4 penalty: 1 off
question
point g is on line segment \\( \overline{fh} \\). given \\( fg = 5x + 2 \\), \\( gh = 3x - 1 \\), and \\( fh = 9 \\), determine the numerical length of \\( \overline{fg} \\).
answer attempt 1 out of 4
\\( fg = \\)
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Explanation:

Step1: Apply segment addition postulate

$FG + GH = FH$

Step2: Substitute given expressions

$(5x + 2) + (3x - 1) = 9$

Step3: Simplify left side

$8x + 1 = 9$

Step4: Solve for x

$8x = 8 \implies x = 1$

Step5: Calculate FG length

$FG = 5(1) + 2$

Answer:

7