NOTES:

|7| is 7

|-7| is 7

Absolute value is ALWAYS a positive number because it represents the distance from zero on a number line

2|x|+1=5

2|x|+1-1=5-1

2|x|=4

|x|=2 by dividing by 2

which means x is 2 OR -2.

This is impossible. |x|=-5. Absolute value cannot be negative. If you get such an answer indicate it does not have a solution by putting -1 in BOTH solution boxes. This is not the answer, it simply indicates you know it is not possible.

What about this?

5|2x+1|+6=41 5|2x+1|=35 (subtract 6 from both sides) |2x+1|=7 (divide by 5)Once you have absolute value equals something you must split into two problems.2x+1=7 OR 2x+1=-7 (absolute value!) 2x=6 OR 2x=-8 (subtract 1 from both sides) x=3 OR x=-4 (divide by 2)

More examples:

|-7x- 8| = 8

Split!

-7x- 8 = 8 or -7x- 8 = -8

-7x = 16 or -7x = 0 (add 8 to both sides)

x=-16/7 or x=0 (divide both sides by -1)

As a decimal (divide using calculator), 16/7 is -2.285.

Since the zero is bigger (further to the right on the number line), it must be put in first for the worksheet to check it.

The answer is x=0 or x=-2.285