Absolute Value Equations & Inequalities

Math - Absolute Value Equations & Inequalities

Absolute value is about the distance a number is from zero. Whether it is a negative number or a positive number using absolute value will always turn the number into a positive number. To solve an equation involving absolute value simply apply the rule that a number will turn positive and treat any absolute value brackets like you would a normal bracket. Remember inequalities describe whether one number is larger or smaller than another. You can treat the inequality sign just like an equal’s sign and do your algebra as normal. But watch out! If you divide by a negative number, then you will need to flip the absolute value sign! This is because you are changing the logic of the mathematical statement

Absolute value inequalities are best illustrated through some examples.

For example:

let's consider. x > |3|

What this expression is trying to say is: A number called {"X"} must be bigger than something we know to be |3|. Whenever someone sees absolute value parameters around something (| |) it means that they must account for two possibilities:

1) the positive value of the absolute value parameter
2) the negative value of the absolute value parameter

So, in nearly all circumstances absolute value inequalities have 2 answers.

So, in our example we will write the solution as this:

Q: x > |3|
A:
x > 3 or x > -3

The answers 3 and -3 comes from evaluating |3|.

Because in an expression of absolute value |3| = 3 and |-3| is also = 3

Example :