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Chapter overview
Learning goals
Learning Goals
Maths
Types of numbers
Number calculations
Fractions, decimals and percentages
Algebraic manipulation
Formulae and equations
Straight line graphs
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Ratio
Proportion
Rates of change
Shapes
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Lines and angles
Drawing shapes
Trigonometry
Probability
Maths
Summary
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.
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.
$x \le 3$ 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 $\ge or \le$
You can use knowledge of rearranging equations to solve the inequalities.
Rearrange like equations to solve.
$\begin {aligned}3x + 10 &\le 22 \\3x &\le 12 \\ \end {aligned}\\ \qquad \underline{x \le 4}$
If you multiply or divide by a negative number, reverse the inequality sign.
$\begin {aligned}-2x &\lt 10 \\ & \qquad \div -2\\ \end {aligned}\\ \quad \underline {x \gt 5}$
Like solving an equation, do the same to each of the 3 parts of the inequality.
$\begin {aligned}21 &\lt 4x-3 &\lt 41 \\&&& +3 \\24 &\lt \quad 4x &\lt 44 \\&&& \div 4 \\\end {aligned}\\ \quad \underline{6 \lt x \lt 11}$
Split the inequality up into two separate questions, solve each separately then recombine the answers.
$\begin {aligned}&&3x-19 &\lt 5x-3 &\lt 4x+2 \\3x-19 &\lt 5x-3 &&& 5x-3 &\lt 4x+2\\-8 &\lt x &&& x &\lt 5\\\end {aligned}$
$\underline {-8 \lt x \lt 5}$
Inequalities 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.
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.
$x \le 3$ 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 $\ge or \le$
You can use knowledge of rearranging equations to solve the inequalities.
Rearrange like equations to solve.
$\begin {aligned}3x + 10 &\le 22 \\3x &\le 12 \\ \end {aligned}\\ \qquad \underline{x \le 4}$
If you multiply or divide by a negative number, reverse the inequality sign.
$\begin {aligned}-2x &\lt 10 \\ & \qquad \div -2\\ \end {aligned}\\ \quad \underline {x \gt 5}$
Like solving an equation, do the same to each of the 3 parts of the inequality.
$\begin {aligned}21 &\lt 4x-3 &\lt 41 \\&&& +3 \\24 &\lt \quad 4x &\lt 44 \\&&& \div 4 \\\end {aligned}\\ \quad \underline{6 \lt x \lt 11}$
Split the inequality up into two separate questions, solve each separately then recombine the answers.
$\begin {aligned}&&3x-19 &\lt 5x-3 &\lt 4x+2 \\3x-19 &\lt 5x-3 &&& 5x-3 &\lt 4x+2\\-8 &\lt x &&& x &\lt 5\\\end {aligned}$
$\underline {-8 \lt x \lt 5}$
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
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