Question

suppose m is the midpoint of (overline{fg}). if (fm = 8x - 3) and (mg = 6x + 1), find the value of x and fg. (x = square) (fg = square)

Explanation:

Step1: Use midpoint property

Since \( M \) is the midpoint of \( \overline{FG} \), \( FM = MG \). So we set up the equation:
\( 8x - 3 = 6x + 1 \)

Step2: Solve for \( x \)

Subtract \( 6x \) from both sides:
\( 8x - 6x - 3 = 6x - 6x + 1 \)
\( 2x - 3 = 1 \)

Add 3 to both sides:
\( 2x - 3 + 3 = 1 + 3 \)
\( 2x = 4 \)

Divide both sides by 2:
\( x = \frac{4}{2} = 2 \)

Step3: Find \( FM \) and \( MG \)

Substitute \( x = 2 \) into \( FM = 8x - 3 \):
\( FM = 8(2) - 3 = 16 - 3 = 13 \)

Substitute \( x = 2 \) into \( MG = 6x + 1 \):
\( MG = 6(2) + 1 = 12 + 1 = 13 \)

Step4: Find \( FG \)

Since \( FG = FM + MG \), and \( FM = MG = 13 \), then:
\( FG = 13 + 13 = 26 \)

Answer:

\( x = 2 \)
\( FG = 26 \)