The smart way to improve grades

Comprehensive & curriculum aligned

Affordable pricing from £10/month

Solve Linear Inequalities

In this worksheet, students will practise solving simple linear inequalities.

'Solve Linear Inequalities' worksheet

Key stage:  KS 4

GCSE Subjects:   Maths

GCSE Boards:   AQA, Eduqas, OCR, Pearson Edexcel

Curriculum topic:   Algebra

Curriculum subtopic:   Solving Equations and Inequalities, Algebraic Inequalities

Difficulty level:  

Worksheet Overview

QUESTION 1 of 10

Inequalities are a branch of algebra that is very closely linked to equations. You will be very familiar by this point of how to solve equations and the good news is that you use exactly the same method to solve inequalities.

What is an inequality?

Inequality just means 'not equal to' so instead of using the = symbol like we do in an equation we use one of the four following symbols.

<     Less than

>     Greater than

≥      Greater than or equal to

≤      Less than or equal to

 

Solving an inequality;

Example 1: Solve  x + 4 < 3

We do this exactly the same way we would an equation.

x + 4 - 4 < 3 - 4

x < -1

What this means is that if you put any number that is less than -1 (-2, -3, -4, -2.1 etc) into the original equation, it would be true.

Example 2: Solve  x/2 > 7

We do this exactly the same way we would an equation.

x/2 x 2 > 7 x 2

x > 14

 

The special case

There is one special case that we need to be aware of. If we had...

5 < x + 3

5 - 3 < x + 3 - 3

2 < x

The issue here is that the x is on the right. If this was an equation, we would just swap them around but we can't quite do that with an inequality.

The inequality currently means '2 is less than x' so if we want the x on the left, we would have to say 'x is greater than 2'.

So 2 < x is the same as x > 2

If you want to switch an inequility over, remember you have to swap the sign.

Which sign will be in the answer for....

x + 3 > 4

>

<

What values of x satisfy the inequality 2x + 8?

>

<

Select from the options below, the values that satisfy the inequality x - 5 ≤ 7.

12

7

15

20

-3

Which of the following is the correct solution set for the inequality...

x / 3 ≥ 2

x ≥ 6

x ≥ 3

x ≤ 6

x ≤ 3

Match the inequality to its set of solutions.

Column A

Column B

x + 4 < 6
x > 2
2x > 8
x < 2
x - 7 > 9
x > 4

Find the set of solutions that satisfy 3 < x + 2.

Column A

Column B

x + 4 < 6
x > 2
2x > 8
x < 2
x - 7 > 9
x > 4

Which of these values will satisfy the inequality 2x  > 4?

0

1

2

3

4

Identify the line in this working with the mistake in it.

 Correctincorrect
2x > 4
Dividing by 2 gives x > 2
This means the answer could be 2 3 4 etc

Which of the following are correct solutions to the inequality 2 ≤ 5x

0

1

2

0.4

-0.4

Complete the following sentence.

0

1

2

0.4

-0.4

  • Question 1

Which sign will be in the answer for....

x + 3 > 4

CORRECT ANSWER
>
EDDIE SAYS
If we aren't moving the x around, the symbol in the answer will be the same as in the question.
  • Question 2

What values of x satisfy the inequality 2x + 8?

CORRECT ANSWER
EDDIE SAYS
This is just a fancy way of saying 'solve the inequality.' All we have to do here is divide both sides by 2
  • Question 3

Select from the options below, the values that satisfy the inequality x - 5 ≤ 7.

CORRECT ANSWER
12
15
-3
EDDIE SAYS
If we solve the inequality, we get the answer x ≤ 12. So we are looking for any numbers that are less than or equal to 12. Don't forget it can equal 12, this is the biggest mistake people make
  • Question 4

Which of the following is the correct solution set for the inequality...

x / 3 ≥ 2

CORRECT ANSWER
x ≥ 6
EDDIE SAYS
To solve this one, we need to remember that the opposite of divide by 3 is to multiply.
  • Question 5

Match the inequality to its set of solutions.

CORRECT ANSWER

Column A

Column B

x + 4 < 6
x < 2
2x > 8
x > 4
x - 7 > 9
x > 2
EDDIE SAYS
It's a nice easy one here. Just remember to do the opposite. If you wanted to get rid of the +4, make sure you - 4. The other thing to remember here is that the sign needs to be the same way around as it is in the question.
  • Question 6

Find the set of solutions that satisfy 3 < x + 2.

CORRECT ANSWER
EDDIE SAYS
Solving the inequality will give 1 < x but we're asked to find it with x first Did you remember to switch the sign?
  • Question 7

Which of these values will satisfy the inequality 2x  > 4?

CORRECT ANSWER
3
4
EDDIE SAYS
Remember that if the sign doesn't have a line underneath, it cannot be that number. Did you select 2?
  • Question 8

Identify the line in this working with the mistake in it.

CORRECT ANSWER
 Correctincorrect
2x > 4
Dividing by 2 gives x > 2
This means the answer could be 2 3 4 etc
EDDIE SAYS
The symbol in the question is greater than, so the answer cannot be 2
  • Question 9

Which of the following are correct solutions to the inequality 2 ≤ 5x

CORRECT ANSWER
1
2
0.4
EDDIE SAYS
Solving the inequality gives 04 ≤ x Switching it around gives x ≥ 0.4 Anything that is 0.4 or above will work
  • Question 10

Complete the following sentence.

CORRECT ANSWER
EDDIE SAYS
Remember that if we want it to mean the same, the sign has to be the opposite.
---- OR ----

Sign up for a £1 trial so you can track and measure your child's progress on this activity.

What is EdPlace?

We're your National Curriculum aligned online education content provider helping each child succeed in English, maths and science from year 1 to GCSE. With an EdPlace account you’ll be able to track and measure progress, helping each child achieve their best. We build confidence and attainment by personalising each child’s learning at a level that suits them.

Get started
laptop

Start your £1 trial today.
Subscribe from £10/month.