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Solve Two-Stage Inequalities

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

'Solve Two-Stage 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 Equations

Difficulty level:  

Worksheet Overview

QUESTION 1 of 10

Finding the solution set for inequalities is quite straight forward as long as you treat them exactly the same as equation.

1) Get rid of things by doing the opposite.

2) Do the same to both sides

 

The main thing that is different (apart from the signs) is that we cannot just move the x to the other side.

In equations 1 = x and x = 1 are the same thing.

In inequalities, if we want to change the side x is on, we have to change the inequality as well.

so 1 < x would be the same as x > 1
 

Example 1: Find the solution set for 3x + 5 ≤ 2

We are trying to get X by itself, so we first need to get rid of the +5, we do this by subtracting 5.

3x + 5 - 5 ≤ 2 - 5

3x ≤ -3

Next, we have to eliminate the multiply by 3, we do this by dividing by 3

3x &div; 3 ≤ -3 &div; 3

x ≤ -1

 

Example 1: Find the solution set for -2 > 3x + 4

We are trying to get X by itself, so we first need to get rid of the +5, we do this by subtracting 5.

-2 - 4 > 3x + 4 - 4

-6 > 3x

Next, we have to eliminate the multiply by 3, we do this by dividing by 3

- 6 &div; 3 > 3x &div; 3

-2 > x

Lastly, this has the x on the right and it needs to be on the left. To do this, we also have to switch the inequality.

x < -2

Which inequality will be in the solution set for 2x + 1 > 5

>

<



Which values of x will satisfy the inequality 3x - 7 < 2

 

(Don't put any spaces in your answer)

Which of the following values satisfy the equation 2x - 7 ≤ 13

1

5

9

10

15

20

Which of these solution sets is correct for the inequality 2x - 3 ≤ 10?

x ≤ 6.5

x ≤ 7

x ≥ 6.6

Match the inequality to its solution set.

Column A

Column B

2x + 3 > 5
x > 1
3x - 2 > 7
x > 1.25
5 < 3x - 1
x > 2
4x - 5 > 0
x > 3

Find the solution set that satisfies...

5 < 3x - 1

Column A

Column B

2x + 3 > 5
x > 1
3x - 2 > 7
x > 1.25
5 < 3x - 1
x > 2
4x - 5 > 0
x > 3

Which of the following values satisfy the equation 2x - 5 > 11

1

5

8

10

15

20

I attempt to solve the equation 3x - 4 > 2.

 

Can you click on the line where I made my first mistake

3x - 4 > 2

3x > -2

3x > -2/3

What is the smallest whole number solution for the inequality...

3 < 4x + 2

What is the largest square number that satisfies the inequality...

3x - 7 < 23

  • Question 1

Which inequality will be in the solution set for 2x + 1 > 5

CORRECT ANSWER
>
EDDIE SAYS
Unless we have to switch the sign (which will only happen if the x is on the right) the sign will be the same.
  • Question 2

Which values of x will satisfy the inequality 3x - 7 < 2

 

(Don't put any spaces in your answer)

CORRECT ANSWER
x<3
EDDIE SAYS
This is just a fancy way of saying find the solution set. Unless the question asks for something else (such as what integers satisfy etc) you just need to do this the same way we did in the equation
  • Question 3

Which of the following values satisfy the equation 2x - 7 ≤ 13

CORRECT ANSWER
1
5
9
10
EDDIE SAYS
Our first step here is to find the solution set. If you do this correctly you should get x ≤ 10 This means any number that is less than or equal to 10 will work for this inequality.
  • Question 4

Which of these solution sets is correct for the inequality 2x - 3 ≤ 10?

CORRECT ANSWER
x ≤ 6.5
EDDIE SAYS
The common mistake people make here is to think that the solution set must be a whole number, If you solve this, you get 6.5 (nothing wrong with this) Remember that the sign will stay the same unless the X is on the right.
  • Question 5

Match the inequality to its solution set.

CORRECT ANSWER

Column A

Column B

2x + 3 > 5
x > 1
3x - 2 > 7
x > 3
5 < 3x - 1
x > 2
4x - 5 > 0
x > 1.25
EDDIE SAYS
Did you remember the rules? 1) Solve it the same way you would an equation 2) Keep the sign the same unless the x is on the right.
  • Question 6

Find the solution set that satisfies...

5 < 3x - 1

CORRECT ANSWER
EDDIE SAYS
Did you notice that the x was on the right? Remember that this means that you have to switch the sign.
  • Question 7

Which of the following values satisfy the equation 2x - 5 > 11

CORRECT ANSWER
10
15
20
EDDIE SAYS
Our first step here is to find the solution set. If you do this correctly you should get x > 8 This means any number that is more than but not equal to 8 will work for this inequality.
  • Question 8

I attempt to solve the equation 3x - 4 > 2.

 

Can you click on the line where I made my first mistake

CORRECT ANSWER
3x > -2
EDDIE SAYS
Did you spot it? I broke one of the main rules for solving inequalities by not doing the opposite,
  • Question 9

What is the smallest whole number solution for the inequality...

3 < 4x + 2

CORRECT ANSWER
1
EDDIE SAYS
Our first step here is to find the solution set. If we do this, we should get x > 0.25 The other part of this question asks for the smallest whole number solution. The first whole number that is bigger than 1 is...
  • Question 10

What is the largest square number that satisfies the inequality...

3x - 7 < 23

CORRECT ANSWER
9
EDDIE SAYS
Our first step here is to find the solution set. If we do this, we should get x < 10 The other part of this question asks for the largest square number that satisfies. The last square number that is smaller than 10 is...
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