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The given problem asks us to complete a two-column proof to show that \( x = 1.25 \), using the diagram and the statements provided. Below is the completed proof with corresponding reasons for each statement:

1. **Statement:** \( H \) is the midpoint of \( FG \).
   - **Reason:** Given

2. **Statement:** \( FH = HG \)
   - **Reason:** Midpoint Theorem (since \( H \) is the midpoint, the segments \( FH \) and \( HG \

Complete the two-column proof to prove that x = 1.25. Given that H is the midpoint of FG and the expressions for FH and HG are 2x + 7 and 12x - 5.5 respectively.

In this proof, learn how to solve for x using the Midpoint Theorem and basic algebraic techniques. The problem demonstrates the geometric concept of a midpoint with algebraic equations, providing a step-by-step explanation for students in Grades 8-10.

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