# Solving inequalities involving modulus

In this post, we’ll look at solving inequalities involving modulus function, and the modulus function is limited to “part” of the expression on either (or both sides ) of the inequality sign.

Examples of such inequalities include:

For such questions, you do not have a single | | on either side or both sides of the inequality sign. However, you have the | | only over certain terms e.g. x. To solve such inequalities, let y = |f(x)|, and solve for y. Once y is solved, you can solve for x.

## Example 1:

Solve the following inequality

Solutions

-3<y < -1 or y > 2

Since y = |x|,

-3<|x|<-1 (reject, since |x|≥ 0 for all values of x) OR |x| > 2 ==> x > 2 or x < -2

Hence, x > 2 or x < -2.

## Example 2:

Solve the following inequality

Solutions

-8<y<-2 or y> 2

Since y = |x|,

-8<|x|<-2 (reject since |x| ≥ 0 for all values of x) OR |x| > 2==> x> 2 or x < -2

Hence, x> 2 or x < -2

## Learn H2 A Level Math Inequalities

Here are the complete notes for solving inequalities for H2 Math:

## All the notes for H2 A Level Math

Go here to find all the notes and resources for H2 A level Math.

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