Absol. val?

Question

Solve for x: | -3x - 6 | = 21
-9 only
-9, 5
9, -5
No solution


12: Solve for x: | -2x - 3 | = -5
1 only
1, -4
No solution
-1, 4


13: Solve | x - 4 | = | 5 - 2x |
1, 3
1 only
3, -3
-1, -3


14: Solve for x: | -2x + 3 | = | x - 15 |
6, -6
6, -12
-6, 12
-6 only


15: Solve for x: | 2x - 4 | + 3 = 5
3 only
-3 only
3, 1
3, -2


16: Solve for x: | 5 - x | = | -x + 3 |
No solution
0, 4
-1, 1
4 only


17: Solve for x: | x/3 - 4 | = 2/3
10, 14
6, 2
-10, -14
-6, -2


18: Solve for x: | x/6 + 5 | + 1/3 = 3/4
0, -5
-25, -30
-55/2, -65/2
0, -9

Answer 1

I will do two for you, and then you will understand and can do the rest (and your OWN homework)

1) | -3x - 6| = 21
The easiest way to think about absolute value is to take both the positive and negative result. So here, what are the answers to
-3x - 6 = 21 and
-3x - 6 = -21?

For the first, -3x - 6 = 21 or -3x = 27 and X = -9
For the second, -3x - 6 = -21, or -3x = -15, and x = 5
So the answer is {-9, 5}.

Similarly,
16. | 5 - x | = |-x + 3| translates to
a) 5 - x = -x + 3 and
b) 5 - x = -(-x + 3) = x - 3 and
c) -(5 -x) = -x + 3, or -5 + x = -x + 3, and
d) -(5 - x) = -(-x + 3), or -5 + x = x - 3.

a) add x to both sides, you get 5 = 3 so this makes no sense. Discard.
b) gets us 5 - x = x - 3 or 5 + 3 = x + x or x = 4
c) gets us -5 + x = -x + 3 or -5 - 3 = -x - x or x = 4
d) subtract x from both sides, you get -5 = -3, discard.
So the answer is {4 only}.

Good luck!