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The midpoint divides the segment into two congruent segments.
AB= 40
We know that M is the midpoint of AB. It is a point that divides the segment into two congruent segments.
Since AM and MB 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+4=RHS+4
.LHS /3.=.RHS /3.
Rearrange equation
The length of AB is equal to the sum of AM and MB. This is a case of the Segment Addition Postulate. AB = AM + MB We can substitute the given values and x=4 into this equation to find AB.
AM= 3x+8, MB= 6x-4
Add terms
x= 4
Multiply
