Modulus Equations

The modulus, or absolute value, of a number is its distance from zero, so it is never negative. That single idea, distance, is the key to solving every modulus equation. Strip away the bars and you are left with two ordinary equations to consider, one for each sign.

In this lesson you will solve equations of the form \(|ax+b|=c\), \(|ax+b|=cx+d\) and \(|ax+b|=|cx+d|\). The guiding rule is simple: if \(|\text{something}|=c\) then that something is \(+c\) or \(-c\). You will also learn the vital habit of checking your solutions, because the modulus can quietly create answers that do not work.