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Inequalities for SQA National 5 Maths

Inequalities

This page covers the following topics:

1. Basics of inequalities
2. Linear inequalities
3. 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

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 y > 11, what are the possible values of y? Assume that y is an integer.

y > 11 means that y is greater than 11; therefore, the possible values of y are 12, 13, 14, 15, 16, โ€ฆ .

12, 13, 14, 15, 16, โ€ฆ

If y > 11, what are the possible values of y? Assume that y is an integer.

2

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

Since the perimeter of the square is less than 30, 4(2x + 5) < 30.
Expanding the left side gives 8x + 20 < 30.
Subtracting both sides by 20 gives 8x < 10.
Dividing both sides by 8 gives x < 1.25.
Since the sides of the square cannot be negative, 2x + 5 > 0.
Subtracting 5 from both sides gives 2x > โˆ’5.
Dividing both sides by 2 gives x > โˆ’5/2.
Putting the two inequalities together gives โˆ’5/2 < x < 5/4.

โˆ’2.5 < x < 1.25

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

3

Solve 3(2x โˆ’ 7) < x โˆ’ 1 and show the range of possible values of x on a number line.

image

Solve 3(2x โˆ’ 7) < x โˆ’ 1 and show the range of possible values of x on a number line.

4

Solve 22x + 8 > 24.

Dividing all terms by 2 gives 11x + 4 > 12.
Subtracting both sides by 4 gives 11x > 8.
Dividing both sides by 11 gives x > 8/11.

x > 8/11

Solve 22x + 8 > 24.

5

Given that z is an integer and z โ‰ฅ โˆ’6, state the possible values of z.

z โ‰ฅ โˆ’6 means that z is greater than or equal to โˆ’6, therefore the possible values of z are โˆ’6, โˆ’5, โˆ’4, โˆ’3, โˆ’2, โ€ฆ .

โˆ’6, โˆ’5, โˆ’4, โˆ’3, โˆ’2, โ€ฆ

Given that z is an integer and z โ‰ฅ โˆ’6, state the possible values of z.

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