QuestionAugust 26, 2025

Equivalent Experience GR.1.1 Unit 1 Suppose M is the midpoint of overline (FG) overline (FM)=3x-4,overline (MG)=5x-26 Find overline (FG) overline (FG)=square

Equivalent Experience GR.1.1 Unit 1 Suppose M is the midpoint of overline (FG) overline (FM)=3x-4,overline (MG)=5x-26 Find overline (FG) overline (FG)=square
Equivalent Experience GR.1.1 Unit 1
Suppose M is the midpoint of overline (FG) overline (FM)=3x-4,overline (MG)=5x-26
Find overline (FG)
overline (FG)=square

Solution
4.1(288 votes)

Answer

58 Explanation 1. Set Midpoint Equation Since M is the midpoint, \overline{FM} = \overline{MG}. Therefore, set 3x - 4 = 5x - 26. 2. Solve for x Rearrange to get 3x - 5x = -26 + 4, which simplifies to -2x = -22. Solving gives x = 11. 3. Calculate Lengths Substitute x = 11 into \overline{FM}: 3(11) - 4 = 33 - 4 = 29. 4. Find Total Length Since \overline{FG} = \overline{FM} + \overline{MG} and both are equal, \overline{FG} = 2 \times 29 = 58.

Explanation

1. Set Midpoint Equation<br /> Since M is the midpoint, $\overline{FM} = \overline{MG}$. Therefore, set $3x - 4 = 5x - 26$.<br />2. Solve for x<br /> Rearrange to get $3x - 5x = -26 + 4$, which simplifies to $-2x = -22$. Solving gives $x = 11$.<br />3. Calculate Lengths<br /> Substitute $x = 11$ into $\overline{FM}$: $3(11) - 4 = 33 - 4 = 29$.<br />4. Find Total Length<br /> Since $\overline{FG} = \overline{FM} + \overline{MG}$ and both are equal, $\overline{FG} = 2 \times 29 = 58$.
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