Question

point h is between g and i. use the segment addition postulate to solve for x when gh = 5x + 2, hi = 26, and gi = 12x + 7. image of segment with points g, h, i options: (a) x=4, (b) x=1, (c) x=3, (d) x=5, (e) x=2 (paraphrased from visible text and structure)

Explanation:

Step1: Apply Segment Addition Postulate

The Segment Addition Postulate states that if \( H \) is between \( G \) and \( I \), then \( GH + HI = GI \). Substituting the given expressions:
\( (5x + 2) + 26 = 12x + 7 \)

Step2: Simplify the left side

Combine like terms:
\( 5x + 28 = 12x + 7 \)

Step3: Subtract \( 5x \) from both sides

\( 28 = 7x + 7 \)

Step4: Subtract 7 from both sides

\( 21 = 7x \)

Step5: Divide both sides by 7

\( x = \frac{21}{7} = 3 \)

Wait, but let's check the options. Wait, maybe I made a mistake? Wait, let's recheck. Wait the options: A. \( x = 4 \), B. \( x = 1 \), C. \( x = 3 \), D. \( x = 5 \), E. \( x = 2 \)? Wait the original problem's options: Let me re-express the steps.

Wait, original equations: \( GH = 5x + 2 \), \( HI = 26 \), \( GI = 12x + 7 \). By Segment Addition: \( GH + HI = GI \)

So \( 5x + 2 + 26 = 12x + 7 \)

Simplify left: \( 5x + 28 = 12x + 7 \)

Subtract \( 5x \): \( 28 = 7x + 7 \)

Subtract 7: \( 21 = 7x \)

Divide by 7: \( x = 3 \). So the correct option is C (assuming C is \( x = 3 \)).

Answer:

C. \( x = 3 \)