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Segments RM and MS are congruent.
Segment Bisector: M RS = 32
We know that segment RM is congruent to MS because they have matching tick-marks. Therefore, the point M is the midpoint and the segment bisector.
Since RM and MS are congruent, the expressions for their lengths must be equal. We can set the two expressions equal to one another and solve for x.
LHS-3x=RHS-3x
LHS+2=RHS+2
.LHS /3.=.RHS /3.
Because M is a midpoint, the length of RS is equal to the sum of RM and MS. This is a case of the Segment Addition Postulate. RS = RM + MS We can substitute the given values and x=3 into this equation to find RS.
RM= 6x-2, MS= 3x+7
Add terms
x= 3
Multiply
