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AQA GCSE Maths Inequalities

Inequalities

This page covers the following topics:

1. Basics of inequalities
2. Number lines
3. Linear inequalities
4. Direction of inequalities

While in an equation the "=" sign indicates that the sides are identical, inequalities are used when they aren't. Different inequalities represent different relationships between the two sides. The definitions of the different symbols that can be used in inequalities are given in the diagram.

Basics of inequalities

Inequalities can be represented on numbre lines, where a hollow dot represents < or >, and a solid dot represents ≀ or β‰₯. To draw a number line, draw a circle over the relevant number, either hollow or solid as appropriate, then draw an arrow in the direction that makes the inequality true, ie. to the left if it is less than or to the right if it is more than.

Number lines

Linear inequalities can be solved just as linear equations using inverse operations, with the only difference being that the inequality sign is kept throughout rather than the "=".

Linear inequalities

When solving inequalities, if it is required to multiply or divide by a negative number, the direction of the inequality sign must be reversed. When there is an expression in terms of the variable that is being solved in the denominator, multiply every term by the square of the expression, so that there is no need to reverse the inequality sign, as this will guarantee that the number that the terms are being multiplied by is positive.

Direction of inequalities

1

If s is an integer and βˆ’2 ≀ s < 2, what are the possible values of s?

If s is an integer and βˆ’2 ≀ s < 2, what are the possible values of s?

2

Solve 50 > 4(8 βˆ’ 2x) βˆ’ x.

Solve 50 > 4(8 βˆ’ 2x) βˆ’ x.

3

Lizzy has 8 more notebooks than Hailey. Given that together they have more than 12 notebooks, found the smallest possible value of the number of notebooks Lizzy has.

Lizzy has 8 more notebooks than Hailey. Given that together they have more than 12 notebooks, found the smallest possible value of the number of notebooks Lizzy has.

4

Given that the perimeter of the triangle is less than its area, give an inequality relating the two quantities.

Given that the perimeter of the triangle is less than its area, give an inequality relating the two quantities.

5

A square of side 2x + 5 has a perimeter less than 30. Find the range of possible values of x.

A square of side 2x + 5 has a perimeter less than 30. Find the range of possible values of x.

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