<PRE><B>Question 9702</B>
Ok, here we go: Get the bars by themselves.

2|3m-1|-12 = 4  Add 12 to both sides.

2|3m-1| = 16 Divide both sides by 2.

|3m-1| = 8  Remove the absolute-value bars and write two equations.

1) 3m-1 = 8 and 
2) 3m-1 = -8

Solve the two equations for m.

1) 3m-1 = 8 add 1 to both sides.
3m = 9 Divide both sides by 3.
m = 3

2) 3m-1 = -8 Add 1 to both sides.
3m = -7 Divide both sides by 3.
m = -7/3 

Check: Remember that |8| = 8 and |-8| = 8

For m = 3:

2|3*3-1|-12 = 4
2|9-1| - 12 = 4
2|8| - 12 = 4
2(8) - 12 = 4
16 - 12 = 4 
4 = 4

For m = -7/3:

2|3(-7/3)-1|-12 = 4
2|-7-1| - 12 = 4
2|-7-1| - 12 = 4
2|-8| - 12 = 4
2(8) - 12 = 4
16 - 12 = 4
4 = 4
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