What is a number line in inequalities?

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

How do you solve inequalities?

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

What are inequalities?

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

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Chapter overview

Learning goals

Maths

Inequalities: Greater than or less than

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Summary

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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

Maths; Formulae and equations; KS3 Year 7; Inequalities: Greater than or less than

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

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

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

Inequalities: Greater than or less than

In a nutshell

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

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Frequently Asked Questions (FAQ)

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

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Inequalities: Greater than or less than

Inequalities: Greater than or less than

In a nutshell

Symbols

Number lines

Solving inequalities

Basic Inequalities

Example 1

Inequalities with negatives

Example 2

Inequalities in two parts

Example 3

Complex Inequalities in two parts

Example 4

Inequalities: Greater than or less than

In a nutshell

Symbols

Number lines

Solving inequalities

Basic Inequalities

Example 1

Inequalities with negatives

Example 2

Inequalities in two parts

Example 3

Complex Inequalities in two parts

Example 4

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

Now you’ve read the summary, have a go at the exercises!