Algebra: Chapter 3-8, page 145.
Solving Equations Involving Absolute Value
The absolute value of a number, `|x|` is its distance from zero on the number line. Remember that the absolute value is always positive. Treat absolute value equations just like those without absolute value and then solve them as normal. At the VERY END, put the absolute value symbols back in and see if the answer has ANOTHER solution.
Remember too, that we cannot have an absolute value be NEGATIVE. In these cases, there is NO SOLUTION. For example:
`|x| + 2 = 12`
`|x| + 2 + (-2) = 12 + (-2)`, we subtract 2 from both sides to isolate the variable, x
`|x| = 10`, we simplify the right side and finally,
`x=10` or `x=-10` are the solutions
This is a good purplemath.com link with examples.