QuestionFind the length of $\overline{F G}$ if $M$ is the midpoint and $F M=12 x-4$ , $M G=5 x+10$ .

Studdy Solution

STEP 1

Assumptions1. $M$ is the midpoint of $\overline{FG}$ , which means $FM = MG$ . . $FM =12x -4$ and $MG =5x +10$ are given.

STEP 2

Since $M$ is the midpoint, $FM = MG$ . We can set up the equation $FM = MG$

STEP 3

Substitute the given expressions for $FM$ and $MG$ into the equation $12x - =5x +10$

STEP 4

olve the equation for $x$ . Start by subtracting $x$ from both sides to get the $x$ terms on one side $12x -x =x +10 -x$ This simplifies to $7x -4 =10$

STEP 5

Next, add $4$ to both sides to isolate the $x$ term $7x =10 +4$ This simplifies to $7x =14$

STEP 6

Finally, divide both sides by to solve for $x $x = \frac{14}{}$ $This simplifies to$ $x =2$ $

STEP 7

Now that we have the value of $x$ , we can find the length of $\overline{FG}$ , which is the sum of $FM$ and $MG$ . $FG = FM + MG$

STEP 8

Substitute the expressions for $FM$ and $MG$ into the equation $FG =12x -4 +5x +10$

STEP 9

Substitute $x =2$ into the equation $FG =12(2) -4 +5(2) +$

STEP 10

Calculate the value of $FG$ $FG =24 -4 +10 +10 =40$ So, the missing measure $FG =40$ .

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