Answer:
CD = 32 units
Step-by-step explanation:
The midpoint divides the segment into congruent parts:
CM = MD
8(x -2) = 4(5x -16)
2(x -2) = 5x -16 . . . . . . divide by 4
2x -4 = 5x -16 . . . . . . . eliminate parentheses
12 = 3x . . . . . . . . . . . . . add 16-2x to both sides
4 = x . . . . . . . . . . . . . . . divide by 3
Then the segment measures are ...
CM = 8(x -2) = 8(4 -2) = 16
CD is twice that length. CD = 32 units.
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Additional comment
There are many ways to solve equations like this. The one usually recommended is to simplify it first. That generally means eliminating parentheses and collecting terms. Doing that would give ...
8x -16 = 20x -64
Since there is a common factor of 4 on both sides, we can divide by that, making the numbers smaller and eliminating one set of parentheses.
Of course, the properties of equality require that whatever operation you perform on one side of the equal sign must also be done on the other side. So "divide by 4" means "divide by 4 on each side of the equal sign."
