Question

the length of (overline{gi}) is equal to (x + 29). given the diagram below, determine its actual length.
diagram: points (g), (h), (i) on a line segment, with (gh = 3x + 5) and (hi = 2x - 12)
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Explanation:

Step1: Find length of \( GI \) as sum of \( GH \) and \( HI \)

\( GI = GH + HI = (3x + 5) + (2x - 12) = 5x - 7 \)

Step2: Set \( GI \) expressions equal and solve for \( x \)

Given \( GI = x + 29 \), so \( 5x - 7 = x + 29 \)
Subtract \( x \): \( 4x - 7 = 29 \)
Add 7: \( 4x = 36 \)
Divide by 4: \( x = 9 \)

Step3: Substitute \( x \) into \( GI = x + 29 \)

\( GI = 9 + 29 = 38 \)

Answer:

38