Advanced Math / Absolute Value Equations
Absolute value equations
An absolute value equation with a positive right side usually splits into two linear equations. A zero right side gives one solution, and a negative right side gives no solution.
Least you need to know
- If $|A|=c$ and $c>0$, then $A=c$ or $A=-c$.
- If $|A|=0$, then $A=0$.
- If $|A|$ equals a negative number, there is no solution.
Key notation
- |x| — The distance from $x$ to 0
Worked example
For $|x-5|=2$, solve $x-5=2$ or $x-5=-2$, giving $x=7$ or $x=3$.
Common mistakes
- Do not split when the right side is negative.
- Remember both branches when the right side is positive.
How to recognize it
- The equation contains absolute value bars and asks for values of $x$.
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