Advanced Math / Absolute Value Equations
Absolute value as distance and solution counts
Absolute value can model distance on a number line. This viewpoint makes solution counts and tolerance statements easier to interpret.
Least you need to know
- Distance is always nonnegative.
- A positive distance from a point gives two locations.
- A distance of zero gives one location.
Key notation
- |x-a| — The distance between $x$ and $a$
Worked example
The statement 'x is within 3 units of 10' is $|x-10|\le 3$.
Common mistakes
- Distance from $a$ is written $|x-a|$, not $|x+a|$.
- Within means at most, not at least.
How to recognize it
- The wording includes distance, within, tolerance, or number of solutions.
Próxima lição recomendada
Continue este tópico com Absolute value equations.
Absolute value equationsLições relacionadas
Continue com lições próximas no mesmo tópico.