Home

Maths

Formulae and equations

Inequalities: Greater than or less than

Select Lesson

Statistics

Qualitative and quantitative data

Representing data: Graphs and charts

Mean, median, mode and range

Frequency tables

Averages from frequency tables

Averages from grouped frequency tables

Scatter graphs

Probability

Calculating probability

Equal and unequal probabilities

Relative frequency

Listing outcomes

Venn diagrams

Trigonometry

Pythagoras’ theorem

Trigonometric ratios: SOH CAH TOA

Finding missing lengths in a triangle

Finding missing angles in a triangle

Drawing shapes

Transformations

Constructions

Constructing triangles

Lines and angles

Types of angles

Angle rules

Interior and exterior angles

Parallel lines

Measures

Area and perimeter: Triangles and quadrilaterals

Area of compound shapes

Volume of prisms

Properties of shapes

Symmetrical shapes and rotational symmetry

Congruent shapes

Similar shapes

Nets and surface area

Shapes

Quadrilaterals: Types and properties

Triangles and regular polygons: Types and properties

Circles: Area and circumference

3D shapes: Identification and properties

Rates of change

Percentage change

Conversion factors

Imperial units

Solving best buy problems

Reading timetables

Maps and scale drawings

Speed: Formula and units

Density: Formula and units

Proportion

Ratio

Other graphs

Interpreting graphs

Solving simultaneous equations using graphs

Quadratic graphs

Travel graphs: Distance-time graphs

Conversion graphs

Straight line graphs

X and Y coordinates

Straight line graphs

Drawing straight line graphs

Finding the gradient

Equation of a straight line: y = mx + c

Drawing a graph of a linear equation

Estimating values using linear graphs

Formulae and equations

Substituting numbers into an expression

Writing and using formulae

Solving equations

Rearranging formulae

Number patterns and sequences

The nth term

Inequalities: Greater than or less than

Simultaneous equations

Algebraic manipulation

Algebraic notation

Algebraic terms

Simplifying algebraic expressions

Multiplying and dividing algebraic expressions

Single brackets: Expanding and factorising

Expanding double brackets: FOIL and multiplication grid

Fractions, decimals and percentages

Converting between fractions, decimals and percentages

Fractions

Fraction operations: Add, subtract, multiply, divide

Percentages

Rounding: Decimal places and significant figures

Rounding errors and estimating

Number calculations

Ordering numbers: Whole numbers and decimals

Addition and subtraction using the column method

Multiplying and dividing by powers of 10

Adding and subtracting decimals

Methods for multiplication and division

Order of operations: BIDMAS

Types of numbers

Understanding place value

Negative numbers: Add, subtract, multiply, divide

Special types of numbers

Multiples, factors and prime factors

Lowest common multiple and highest common factor

Square roots and cube roots

Writing indices and index laws

Standard form

Explainer Video

Tutor: Meera

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

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

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

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

Learn with Basics

Length:

Unit 1

Inverse operations to check calculations

Unit 2

Solving equations

Jump Ahead

Optional

Unit 3