Answer:
- x = 8
- AM = 64 cm
- BM = 64 cm
- M is the midpoint
Explanation:
Part A. The total length of a line segment is the sum of the lengths of its parts.
AM +MB = AB
Substituting the given information, this equation becomes ...
(7x +8) cm + (9x -8) cm = 128 cm
16x = 128 . . . . . . . . . collect terms, divide by cm
x = 128/16 . . . . . divide by the coefficient of x
x = 8
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Part B. Then the length of AM is ...
AM = (7x +8) cm = (7(8) +8) cm = (56 +8) cm
AM = 64 cm
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Part C. The length of BM is ...
BM = (9x -8) cm = (9(8) -8) cm = (72 -8) cm
BM = 64 cm
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Part D. AM = BM = 64 cm, so point M is the midpoint of AB. Point M divides the segment into two equal parts.