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Maths Quiz - Level 7-8 Algebra - Inequalities (Questions)

Inequalities compare values using <, >, ≤, or ≥. Learn to solve, show solutions on number lines, and interpret real contexts in KS3 Maths.

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Fascinating Fact:

A road sign that says “Speed limit 30 mph” is an inequality written as speed ≤ 30, meaning drivers must stay at or below 30 mph.

In KS3 Maths, inequalities show when one value is bigger, smaller, or limited by another. You’ll solve one- and two-step inequalities, represent solution sets on number lines, and apply them to real situations.

Key Terms

Inequality: A statement comparing two quantities using symbols like <, >, ≤, or ≥.
Solution set: All values that make an inequality true (often shown on a number line).
Number line: A line used to show solutions with open/closed circles and arrows for ranges.

Frequently Asked Questions (Click to see answers)

How do you solve a one-step inequality like x + 5 < 12?

Undo the operation on x. Subtract 5 from both sides: x + 5 < 12 becomes x < 7. Show this on a number line with an open circle at 7 and shading left.

What does x ≤ 7 mean on a number line?

x ≤ 7 means all numbers up to and including 7. Use a filled (closed) circle at 7 and shade to the left to show every value less than or equal to 7.

When do you reverse the inequality sign in KS3?

Reverse the sign when you multiply or divide both sides by a negative number. For example, from -2x > 8 you get x < -4.

Try These Related Quizzes

1.

< is the sign that means what?

[ ]	Less than
[ ]	Greater than
[ ]	Less than or equal to
[ ]	Greater than or equal to

2.

> is the sign that means what?

[ ]	Less than
[ ]	Greater than
[ ]	Less than or equal to
[ ]	Greater than or equal to

3.

≤ is the sign that means what?

[ ]	Less than
[ ]	Greater than
[ ]	Less than or equal to
[ ]	Greater than or equal to

4.

≥ is the sign that means what?

[ ]	Less than
[ ]	Greater than
[ ]	Less than or equal to
[ ]	Greater than or equal to

5.

If x > 3, what is the smallest integer that x can be?

[ ]	2
[ ]	3
[ ]	4
[ ]	5

6.

If x ≥ 19, which of the following numbers is not possible for the value of x?

[ ]	18
[ ]	19
[ ]	20
[ ]	21

7.

If 4x + 3 < 15, which of the following expressions are incorrect?

[ ]	4x < 15 - 3
[ ]	4x < 12
[ ]	x < 3
[ ]	x > 3

8.

If 4x - 7 < 17, which of the following expressions are incorrect?

[ ]	4x < 17 + 7
[ ]	4x < 24
[ ]	x > 6
[ ]	x < 6

9.

If 16x - 5 > 59, which of the following is correct?

[ ]	16x > 64
[ ]	16x > 59
[ ]	16x < 59
[ ]	16x < 64

10.

If 9x + 40 > 140 which of these is correct?

[ ]	9x - 40 > 140
[ ]	9x > 100
[ ]	9x < 100
[ ]	x > 20

You can find more about this topic by visiting BBC Bitesize - Inequalities

Maths Quiz - Level 7-8 Algebra - Inequalities (Answers)

1.

< is the sign that means what?

[x]	Less than
[ ]	Greater than
[ ]	Less than or equal to
[ ]	Greater than or equal to

This might help you remember which way the less than sign points: Less = Left (pointing)

2.

> is the sign that means what?

[ ]	Less than
[x]	Greater than
[ ]	Less than or equal to
[ ]	Greater than or equal to

The small end of the sign always points to the smaller number

3.

≤ is the sign that means what?

[ ]	Less than
[ ]	Greater than
[x]	Less than or equal to
[ ]	Greater than or equal to

Numbers that are < 6 are 5, 4, 3 etc; numbers that are ? 6 are 6, 5, 4, etc. Can you see the difference? If not then look again because it is important that you understand the difference between these signs

4.

≥ is the sign that means what?

[ ]	Less than
[ ]	Greater than
[ ]	Less than or equal to
[x]	Greater than or equal to

Remember, the arrow always points to the smaller number

5.

If x > 3, what is the smallest integer that x can be?

[ ]	2
[ ]	3
[x]	4
[ ]	5

x must be greater than three and the next integer after three is four

6.

If x ≥ 19, which of the following numbers is not possible for the value of x?

[x]	18
[ ]	19
[ ]	20
[ ]	21

18 is less than 19

7.

If 4x + 3 < 15, which of the following expressions are incorrect?

[ ]	4x < 15 - 3
[ ]	4x < 12
[ ]	x < 3
[x]	x > 3

When a number crosses over the < or > signs then it changes from positive to negative or vice versa

8.

If 4x - 7 < 17, which of the following expressions are incorrect?

[ ]	4x < 17 + 7
[ ]	4x < 24
[x]	x > 6
[ ]	x < 6

Values for x are less than 6

9.

If 16x - 5 > 59, which of the following is correct?

[x]	16x > 64
[ ]	16x > 59
[ ]	16x < 59
[ ]	16x < 64

It is extremely easy to mix-up < and > so be careful!

10.

If 9x + 40 > 140 which of these is correct?

[ ]	9x - 40 > 140
[x]	9x > 100
[ ]	9x < 100
[ ]	x > 20

If 9x + 40 > 140 then 9x must be > 100