If R is the midpoint of line segment ST, and SR = 3x + 8 and RT = 5x - 6, what is the measure of the line segment SR?

To find the measure of the line segment SR, we start with the information that R is the midpoint of segment ST. This implies that the lengths of segments SR and RT are equal because a midpoint divides a segment into two equal parts. Therefore, we can set up the equation:

[ SR = RT ]

Given that ( SR = 3x + 8 ) and ( RT = 5x - 6 ), we can write:

[ 3x + 8 = 5x - 6 ]

Next, we need to solve for ( x ). We can rearrange the equation:

1. Subtract ( 3x ) from both sides:

[ 8 = 2x - 6 ]

2. Add 6 to both sides:

[ 14 = 2x ]

3. Divide both sides by 2:

[ x = 7 ]

Now that we have the value of ( x ), we can substitute it back into the expression for ( SR ):

[ SR = 3x + 8 ]

[ SR = 3(7) + 8 ]

[ SR = 21 + 8 ]

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