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Solve One Step Equations

In this worksheet, students will learn how to solve simple one-step linear equations.

'Solve One Step Equations' worksheet

Key stage:  KS 4

GCSE Subjects:   Maths

GCSE Boards:   Pearson Edexcel, OCR, Eduqas, AQA

Curriculum topic:   Algebra

Curriculum subtopic:   Solving Equations and Inequalities, Algebraic Expressions

Difficulty level:  

Worksheet Overview

QUESTION 1 of 10

"I think of a number, add 9 and the answer is 23. What number am I thinking of?"

 

Have you ever played games like this? You may not realize it but when you work out the answer you are actually solving an equation. If we use a letter (usually x) for the unknown number then we can write the problem as an equation.

 

x + 9 = 23

 

Now, to find what x is we have to work backwards from the answer remembering that subtracting is the opposite (or inverse) of adding. When we write down our solution to an equation it is important that we show our working. This is particularly important as the equations get harder, and you can get marks for this in an exam!
 

Think of an equation as a set of old fashioned weighing scales which balance.

 

If you add or take something from one side of the scales it will upset the balance unless you so the same thing to the other side. When we solve an equation we are trying to get the x by itself on the left-hand side. To do this we must remove the +9 by doing the inverse which is -9. However, this will upset the balance unless we -9 from the right-hand side as well. We set this out as follows:

So the solution to the equation is x = 14

 

Let's try another equation:

 

6x = 48

 

What does 6x mean?  It means 6 multiplied by x.

 

Remember the scales, what we do to one side of the equation, we must do to the other.  Since the inverse of multiply is divide we set out our working as follows:

Remember x is not always used as the unknown, examiners could use any letter, but the principle is still the same!  Let's give this a go!

 

 

 

Choose the correct solution to the equation

x - 19 = 11

x = -8

x = 8

x = 20

x = 30

Here's an equation with a different letter.

g + 3 = 12

Which of these is the correct solution?

 

g = -9

g = 4

g = 9

g = 15

Can you solve the equation 7d = 56?

 

Solve the following equation.

z + 37 = 56

Can you match the following equations to their solutions?

Column A

Column B

x + 4 = 12
x = 16
x - 4 = 12
x = 2
4x = 12
x = 3
4 - x = 2
x = 8

Can you match each equation to its solution?

Column A

Column B

8w = 4
w = 0.5
4w = 8
w = 2
w ÷ 4 = 8
w = -4
w + 8 = 4
w = 32

p = 8 is the solution to which of these equations. There may be more than one correct answer here.   

p + 8 = 16

p - 8 = 16

8p = 16

16 ÷ p = 2

p ÷ 16 = 2

Which of these equations has the solution x = -4 (you may choose more than one)?

x + 4 = 0

-3x = 12

x - 4 = 0

2x = -8

4 - x = 0

Can you match the equations to their solutions? 

Solve the equation. 

27 - x = 74

  • Question 1

Choose the correct solution to the equation

x - 19 = 11

CORRECT ANSWER
x = 30
EDDIE SAYS
Remember to get x on its own first. To do this you need to add 19 to the left-hand side, so make sure you do that to the right also. x -19 = 11 +19 +19 x = 30
  • Question 2

Here's an equation with a different letter.

g + 3 = 12

Which of these is the correct solution?

 

CORRECT ANSWER
g = 9
EDDIE SAYS
How did you do? The inverse of '+3' is '-3' so the solution is: x + 3 = 12 -3 -3 x = 9
  • Question 3

Can you solve the equation 7d = 56?

 

CORRECT ANSWER
d = 8
d=8
d =8
d= 8
8
EDDIE SAYS
Remember if there is a number right before a letter this means that the number should multiply that letter. For example here, 7d = d X 7. The inverse of times 7 is divide by 7. 7d = 56 ÷​ 7 ÷​ 7 d = 8
  • Question 4

Solve the following equation.

z + 37 = 56

CORRECT ANSWER
EDDIE SAYS
Remember to go through the phases outlined in the introduction. Always remember the scales, what you do to one side, you must do to the other! z + 37 = 56 (Subtract 37 from the right - hand side to get z, do this to the left too!) z = 56-37 z = 19
  • Question 5

Can you match the following equations to their solutions?

CORRECT ANSWER

Column A

Column B

x + 4 = 12
x = 8
x - 4 = 12
x = 16
4x = 12
x = 3
4 - x = 2
x = 2
EDDIE SAYS
To be sure you are right here, it is best to grab a pen and some paper and work first. Just remember the key steps to solving equations. x + 4 = 12 → both sides -4 → x = 8 x - 4 = 12 → both sides +4 → x = 16 4x = 12 → both sides ÷4 → x = 3 4 - x = 2 → both sides -4 → -x = -2 so x = 2
  • Question 6

Can you match each equation to its solution?

CORRECT ANSWER

Column A

Column B

8w = 4
w = 0.5
4w = 8
w = 2
w ÷ 4 = 8
w = 32
w + 8 = 4
w = -4
EDDIE SAYS
Did you work this out first on paper? Remember in an exam you will be given marks for showing your working. 8w = 4 → both sides ÷8 → w = 0.5 4w = 8 → both sides ÷4 → w = 2 w/4 = 8 → both sides x4 → w = 32 w + 8 = 4 → both sides -8 → w = -4
  • Question 7

p = 8 is the solution to which of these equations. There may be more than one correct answer here.   

CORRECT ANSWER
p + 8 = 16
16 ÷ p = 2
EDDIE SAYS
We can check each equation by replacing the p with 8 and seeing if it gives the right answer. p + 8 = 16 → 8 + 8 = 16 (correct) p - 8 = 16 → 8 - 8 = 0 (wrong) 8p = 16 → 8 x 8 = 64 (wrong) 16 ÷ p = 2 → 16 ÷ 8 = 2 (correct) p ÷16 = 2 → 8 ÷ 16 = 0.5 (wrong) So two of them were correct. Did you get them both?
  • Question 8

Which of these equations has the solution x = -4 (you may choose more than one)?

CORRECT ANSWER
x + 4 = 0
-3x = 12
2x = -8
EDDIE SAYS
Remember, you can check each equation by replacing x with -4. x + 4 = 0 → -4 + 4 = 0 (correct) -3x = 12 → -3 x -4 = 12 (correct) x - 4 = 0 → -4 - 4 = -8 (wrong) 2x = -8 → 2x-4 = -8 (correct) 4 - x = 0 → 4 - -4 = 8 (wrong) [Remember a double minus makes a plus] So this time there were three correct answers. How did you do?
  • Question 9

Can you match the equations to their solutions? 

CORRECT ANSWER
EDDIE SAYS
Lets work out each equation to see which solution matches. 6c = 3 → divide by 6 → c = 0.5 c + 5 = 2 → subtract 5 → c = -3 c - 5 = -5 → add 5 → c = 0 5c = 1 → divide by 5 → c = 1 ÷ 5 = 0.2
  • Question 10

Solve the equation. 

27 - x = 74

CORRECT ANSWER
x = -47
EDDIE SAYS
This last one is a tricky one as the x is subtracted from 27. It's not the same as 27 - x. Start by subtracting 27 from both sides. 27 - x = 74 - 27 -27 -x = 57 Don't forget you still have the 'minus' sign infront of the x. If -x is 57 then the opposite is also true, so...... x = -57 Well done, that's a whole exercise completed on solving equations, hope you are feeling more confident now? Remember to always write down your workings!
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