Question

suppose m is the midpoint of $overline{fg}$. find the missing measure.
$fm = 3x - 4, mg = 5x - 26$
$fg=square$

Explanation:

Step1: Use mid - point property

Since $M$ is the mid - point of $\overline{FG}$, then $FM = MG$. So we set up the equation $3x−4 = 5x−26$.
$3x−4=5x - 26$

Step2: Solve for $x$

Subtract $3x$ from both sides:
$-4 = 5x-3x - 26$
$-4 = 2x-26$
Add 26 to both sides:
$2x=-4 + 26$
$2x = 22$
Divide both sides by 2:
$x=\frac{22}{2}=11$

Step3: Find $FM$ and $MG$

Substitute $x = 11$ into the expression for $FM$: $FM=3x - 4=3\times11-4=33 - 4 = 29$
Since $FM = MG$, then $MG = 29$

Step4: Find $FG$

Since $FG=FM + MG$ and $FM = MG = 29$, then $FG=29+29 = 58$

Answer:

$58$