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Solve Inequalities (on a number line)

In this worksheet, students will practise solving inequalities and putting them on a number line.

'Solve Inequalities (on a number line)' worksheet

Key stage:  KS 4

Curriculum topic:  

Curriculum subtopic:  

Difficulty level:  

Worksheet Overview

QUESTION 1 of 10

 

When we are dealing with inequalities, one of the things we have to do is to state all the numbers that satisfy an inequality. We can either do this by giving a solution set or by drawing the numbers on a number line.

Example 1: Illustrate the inequality 3x – 4 > 2 on a number line.

The first step here is to solve the inequality.

3x – 4 + 4> 2 + 4

3x > 6

3x ÷ 3 > 6 ÷ 3

x > 2

Now we have the solution set, we can draw this on a number line.

As the inequality is greater than, we use an unshaded circle to show the value of 2. We know that the solutions are greater than 2, so we draw an arrow to the right.

 

Example 2: Illustrate the inequality 2x + 1 ≤ 5 on a number line.

The first step here is to solve the inequality.

2x + 1 ≤ 5

2x + 1 -1 ≤ 5 - 1

2x ≤ 4

2x ÷ 2 ≤ 4 ÷ 2

x ≤ 2

Now we have the solution set, we can draw this on a number line.

As the inequality is less than or equal to, we use a shaded circle to show the value of 2. We know that the solutions are less than or equal 2, so we draw an arrow to the left.

 

Example 2: Illustrate the inequality -1 ≤ 2x – 3 < 5 on a number line.

The first step here is to solve the inequality.

-1 + 3 ≤ 2x – 3 + 3 < 5 + 3

2 ≤ 2x < 8

2 ÷ 2  ≤ 2x ÷ 2  < 8 ÷ 2

1 ≤ x < 4

Now we have the solution set, we can draw this on a number line.

We can see that the solutions are between 1 and 4. The circle at 1 has to be shaded as it is ≤ and the one at 4 has to be unshaded.

When illustrating an inequality...

When illustrating an inequality...

What is the solution set for 2x + 1 < 5

 

(Don’t put any spaces in your answer)

Which of these number lines show the correct solution for 2x + 1 < 5?

 



What is the solution set for 3x – 5 ≥ -8



Which of these number lines show the solution set of 3x – 5 ≥ -8

 

A

B

C

D

What is the solution set for 5x + 3 > 2x + 9

 

(Don’t put any spaces in your answer)

 

ANS: x > 2

Which of these number lines show the solution set of 5x + 3 > 2x + 9

 

A

B

C

D

Match the solution set with the illustration on the number line.

 

Column A

Column B

x > 4

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x < -1

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x ≥ -1

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Match the inequality with the solution set

Column A

Column B

2x – 5 < 3
x < -1
2x – 5 > -7
x > 4
2x – 5 > -9
x > -2
  • Question 1

When illustrating an inequality...

CORRECT ANSWER
EDDIE SAYS
When we are dealing with < or >, we can’t have the number as part of our solution set. We show this by not shading the circle.
  • Question 2

When illustrating an inequality...

CORRECT ANSWER
EDDIE SAYS
When we are dealing with ≥ or ≤ we must have the number as part of our solution set. We show this by shading the circle.
  • Question 3

What is the solution set for 2x + 1 < 5

 

(Don’t put any spaces in your answer)

CORRECT ANSWER
x<2
EDDIE SAYS
We need to solve this in the same way we would solve an equation. We subtract 1 from both sides We divide both sides by 2 This will give the solution x < 2
  • Question 4

Which of these number lines show the correct solution for 2x + 1 < 5?

 

CORRECT ANSWER

EDDIE SAYS
If we solve this inequality, we get a solution set of x <2. Because the inequality is <, we use an unshaded circle and our arrow goes to the left.
  • Question 5

What is the solution set for 3x – 5 ≥ -8

CORRECT ANSWER
EDDIE SAYS
Again, we solve this the same way as we would an equation. Add 5 to both side Divide both sides by 3 Remember that the inequality remains the same.
  • Question 6

Which of these number lines show the solution set of 3x – 5 ≥ -8

 

CORRECT ANSWER
C
EDDIE SAYS
Solving this inequality gives the solution set x ≥ -1 From this, we can see that the arrow should be pointed to the right and the circle should be shaded.
  • Question 7

What is the solution set for 5x + 3 > 2x + 9

 

(Don’t put any spaces in your answer)

 

ANS: x > 2

CORRECT ANSWER
x>2
EDDIE SAYS
The only difference here is that we have unknowns on both sides. This means our first step is to eliminate one of them. This would give the inequality 3x + 3 > 9 which can then be solved as before.
  • Question 8

Which of these number lines show the solution set of 5x + 3 > 2x + 9

 

CORRECT ANSWER
A
EDDIE SAYS
Solving the inequality 5x + 3 > 2x + 9 gives the solution set of x > 2. This tells us that the arrow goes to the right and the circle will be unshaded.
  • Question 9

Match the solution set with the illustration on the number line.

 

CORRECT ANSWER

Column A

Column B

x > 4

');" onmouseout="tooltip.hide();">

x < -1

');" onmouseout="tooltip.hide();">

x ≥ -1

');" onmouseout="tooltip.hide();">

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EDDIE SAYS
With these, you can either approach by looking at the inequality (there’s only one that is greater than or equal to) and matching it with if the circle has been shaded or you can match the number first. (One of them has a different number to the others.)
  • Question 10

Match the inequality with the solution set

CORRECT ANSWER

Column A

Column B

2x – 5 < 3
x > 4
2x – 5 > -7
x < -1
2x – 5 > -9
x > -2
EDDIE SAYS
While this looks quite difficult at first glance, we can just follow the same rules. Add 5 to both sides Divide both sides by 2
---- OR ----

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