The smart way to improve grades

Comprehensive & curriculum aligned

Affordable pricing from £10/month

Solve Complex Inequalities

In this worksheet, students will practise solving multi-stage inequalities.

'Solve Complex 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

Solving inequalities is very simple if you follow a few simple rules.

1) Deal with them the same way as an equation.

2) If you want to switch the x in a solution set, you have to switch the sign (i.e. 1 > x is the same as x > 1)

 

A quick word on the language, when you are dealing with equations, you aren't finding a solution (this is for equations), you are finding a solution set.

 

Example 1: Find the solutions for 2x + 1 < 5x + 3

Step 1: We have a value of x on both sides, so we have to get rid of one of them, always get rid of the smaller one (this helps to avoid negatives)

3x + 1 < 5x + 3

3x + 1 - 3x < 5x + 3 - 3x

1 < 2x + 3

Step 2: Isolate the X

1 < 2x + 3

1 - 3 < 2x + 3 - 3

-2 <  2x

-2 ÷ 2<  2x ÷ 2

-1 < x

Step 3: Switch the inequality if necessary

x > -1

 

Example 2: Find the solutions for -5 ≤ 3x + 1 ≤ 7

We have three parts here, the key thing to remember is that we have to do the same to all the parts of the inequality

-5 ≤ 3x + 1 ≤ 7

-5 - 1 ≤ 3x + 1 - 1 ≤ 7 - 1

-6 ≤ 3x ≤ 6

-6 ÷ 3≤ 3x ÷ 3 ≤ 6 ÷ 3

-2 ≤ x ≤ 2

For an inequality such as 2x + 1 < 5x + 3. Our first step is to...

When we are solving a three part inequality, we...

Do the same to both sides

Do the same to all three parts

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

 

6x - 4 > 3x + 11

x > 5

x < 5

Which of the following numbers are in the solution set for the nequality...

19 ≤ 4x + 3 < 23

4

4.2

4.6

5

Find the solution set for 5x + 1 < 3x + 5

Find the solution set for the inequality 3 < 3x < 9

 

(Don't put any spaces in your answer)

 

Match the inequality with it's solution set.

Column A

Column B

6x + 1 > 2x + 9
x < 2
2x + 2 < 14 - x
x > 2
x + 8 > 6x - 4
x < 4

Match the inequality with it's solution set.

Column A

Column B

7 < 3x + 1 < 16
2 < x < 5
-1 < x < 3
-7 < 4x - 3 < 9
-9 < 5x + 6 < 1
-3 < x < -1

Find the solution set for 4x - 7 > 6x - 13

 

(Don't put any spaces in your answer)

Find the solution set for 7 < 4x - 5 < 17

 

(Don't put any spaces in your answer)

  • Question 1

For an inequality such as 2x + 1 < 5x + 3. Our first step is to...

CORRECT ANSWER
EDDIE SAYS
We have to get this in a form we can deal with. We need to combine (or eliminate) the terms.
  • Question 2

When we are solving a three part inequality, we...

CORRECT ANSWER
Do the same to all three parts
EDDIE SAYS
It's a common mistake with these questions to do something to both sides (this is what you have to do with equation) In a three part, you have to do the same to all the parts of the inequality
  • Question 3

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

 

6x - 4 > 3x + 11

CORRECT ANSWER
x > 5
EDDIE SAYS
This is alot easier than it looks. As the larger value of X is on the right, we aren\'t going to have to swittch at the end. This means the symbol in the middle will stay the same.
  • Question 4

Which of the following numbers are in the solution set for the nequality...

19 ≤ 4x + 3 < 23

CORRECT ANSWER
4
4.2
4.6
EDDIE SAYS
The first step is to solve this inequality. 4 ≤ x < 5 So the numbers in our solution set are larger than OR EQUAL TO 4 and smaller than 5
  • Question 5

Find the solution set for 5x + 1 < 3x + 5

CORRECT ANSWER
x<2
x < 2
x< 2
x <2
EDDIE SAYS
This is the most common type of question you will face. Just remember the rules. 1) Eliminate one of the terms in x 2) Get X by itself by doing the same to both sides 3) Rearrange the inequality if necessary
  • Question 6

Find the solution set for the inequality 3 < 3x < 9

 

(Don't put any spaces in your answer)

 

CORRECT ANSWER
1
EDDIE SAYS
Another nice and easy one. As it's a three parter, we just have to do the same (divide by 3 in this case) to all the parts of the inequality.
  • Question 7

Match the inequality with it's solution set.

CORRECT ANSWER

Column A

Column B

6x + 1 > 2x + 9
x > 2
2x + 2 < 14 - x
x < 4
x + 8 > 6x - 4
x < 2
EDDIE SAYS
This is the most common type of question you will face. Just remember the rules. 1) Eliminate one of the terms in x 2) Get X by itself by doing the same to both sides 3) Rearrange the inequality if necessary
  • Question 8

Match the inequality with it's solution set.

CORRECT ANSWER

Column A

Column B

7 < 3x + 1 < 16
2 < x < 5
-1 < x < 3
-7 < 4x - 3 < 9
-9 < 5x + 6 < 1
-3 < x < -1
EDDIE SAYS
Another nice and easy one. As it's a three parter, we just have to do the same (divide by 3 in this case) to all the parts of the inequality.
  • Question 9

Find the solution set for 4x - 7 > 6x - 13

 

(Don't put any spaces in your answer)

CORRECT ANSWER
x<3
EDDIE SAYS
This is the most common type of question you will face. Just remember the rules. 1) Eliminate one of the terms in x 2) Get X by itself by doing the same to both sides 3) Rearrange the inequality if necessary
  • Question 10

Find the solution set for 7 < 4x - 5 < 17

 

(Don't put any spaces in your answer)

CORRECT ANSWER
3
EDDIE SAYS
Another nice and easy one. As it's a three parter, we just have to do the same (divide by 3 in this case) to all the parts of the inequality. Don't worry about the last number being a decimal. It's perfectly valid.
---- 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.

  • educational
  • bettfutures
  • cxa
  • pta
  • era2016
  • BDA award
  • Explore LearningTuition Partner
  • tacm