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Maths

# Inequalities: Greater than or less than 0%

Summary

# Inequalities: Greater than or less than

## In a nutshell

Inequalities show when one expression is greater than or less than another expression. Inequalities with more complex expressions can be solved in a similar way to equations. The answers can be represented algebraically or on a number line.

## Symbols

Inequalities involve using symbols to describe the relationship between two expressions.

SYMBOL

DESCRIPTION

$\lt$​​
less than
$\le$​​
less than or equal to
$\gt$​​
greater than
$\ge$​​
greater than or equal to

Note: The arrow points to the smaller number.

## Number lines

$x \le 3$ means that $x$ is less than or equal to $3$. It can be represented by the number line

use $\circ$ for $\gt or \lt$

use $\bullet$ for $\ge or \le$

## Solving inequalities

You can use knowledge of rearranging equations to solve the inequalities.

### Basic Inequalities

Rearrange like equations to solve.

##### Example 1

\begin {aligned}3x + 10 &\le 22 \\3x &\le 12 \\ \end {aligned}\\ \qquad \underline{x \le 4}​​

### Inequalities with negatives

If you multiply or divide by a negative number, reverse the inequality sign.

##### Example 2

\begin {aligned}-2x &\lt 10 \\ & \qquad \div -2\\ \end {aligned}\\ \quad \underline {x \gt 5}​​

### Inequalities in two parts

Like solving an equation, do the same to each of the 3 parts of the inequality.

##### Example 3

\begin {aligned}21 &\lt 4x-3 &\lt 41 \\&&& +3 \\24 &\lt \quad 4x &\lt 44 \\&&& \div 4 \\\end {aligned}\\ \quad \underline{6 \lt x \lt 11}​​

### Complex Inequalities in two parts

Split the inequality up into two separate questions, solve each separately then recombine the answers.

##### Example 4

\begin {aligned}&&3x-19 &\lt 5x-3 &\lt 4x+2 \\3x-19 &\lt 5x-3 &&& 5x-3 &\lt 4x+2\\-8 &\lt x &&& x &\lt 5\\\end {aligned}

$\underline {-8 \lt x \lt 5}$

## Want to find out more? Check out these other lessons!

Solving equations

FAQs

• Question: What is a number line in inequalities?

Answer: A number line is a visual way to show the solution to an inequality.

• Question: How do you solve inequalities?

Answer: Inequalities can be solved in a similar way to solving equations by rearranging.

• Question: What are inequalities?

Answer: Inequalities show when one expression is greater than or less than another expression. They can be represented algebraically, or on a number line.

Theory

Exercises