Algebra 9_3b - Solving Absolute Value Equations.

Provide the value for x in the solution boxes. Put the higher value in the first box. If impossible, put -1 in BOTH solution boxes. See notes at the bottom of the page. YOU MAY GET FRACTIONS, put in as a decimal rounded to three places (see last example at bottom)

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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.

```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