Algebra 3_8b - 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.

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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.

What about this?

5|2x+1|+6=41
5|2x+1|=35  (subtract 6 from both sides)
|2x+1|=7   (divide by 5)
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)