Answer:
1. m = -10/3 or 2
2. x = 5/2 or -1
Explanation:
An absolute value function such as ...
|x| = a
resolves to two equations:
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1. |-2-3m| = 8
First case:
-2 -3m = 8
-3m = 10
m = -10/3
Second case:
-2 -3m = -8
-3m = -6
m = 2
Solutions are m = -10/3 or 2.
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2. 4|4x-3| -4 = 24
Divide by 4 and add 1:
|4x -3| -1 = 6
|4x -3| = 7
First case:
4x -3 = 7
4x = 10 . . . . add 3
x = 10/4 = 5/2 . . . . divide by 4, reduce the fraction
Second case:
4x -3 = -7
4x = -4 . . . . add 3
x = -1 . . . . . divide by 4
Solutions are x = 5/2 or -1.