 # Solve One Step Equations

In this worksheet, students will learn how to solve one-step equations by finding the value of one unknown element represented by a letter. 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:   ### 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 realise 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, like this:

e.g. 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 even 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 with our example above, 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 these steps out like this: So the solution to the equation is: x = 14

Let's try another equation now:

e.g. 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 letter to represent the unknown element, any letter could be used but the principle is still the same!

Let's give this a go now!

In this activity, we will solve equations by finding the value of one unknown element represented by a letter.

Choose the correct solution to the equation below:

x - 19 = 11

x = -8

x = 8

x = 20

x = 30

Here's an equation with a different letter:

g + 3 = 12

Which of the options below is the correct solution?

g = -9

g = 4

g = 9

g = 15

Can you solve the equation below?

7d = 56

Write the value of d as a number below.

g = -9

g = 4

g = 9

g = 15

Solve the equation below.

z + 37 = 56

g = -9

g = 4

g = 9

g = 15

Can you match each of the equations below to their correct solution?

## Column B

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

Can you match each of the equations below to their correct solution?

## Column B

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

p = 8 is the solution to an equation.

Which of the equations below has this solution?

p + 8 = 16

p - 8 = 16

8p = 16

16 ÷ p = 2

p ÷ 16 = 2

x = - 4 is the solution to an equation.

Which of the equations below has this solution?

x + 4 = 0

-3x = 12

x - 4 = 0

2x = -8

4 - x = 0

Can you match each equation below to its correct solution?

Solve the equation below:

27 - x = 74

• Question 1

Choose the correct solution to the equation below:

x - 19 = 11

x = 30
EDDIE SAYS
Firstly, we need to get x on its own. To do this, we need to add 19 to the left-hand side. Can you remember our balance scales in the Introduction? If we apply a change to one side, we need to do the same on the other. So here we need to take 19 away from both sides. x - 19 = 11 x - 19 + 19 = 11 - 19 x = 30
• Question 2

Here's an equation with a different letter:

g + 3 = 12

Which of the options below is the correct solution?

g = 9
EDDIE SAYS
How did you do here? The inverse of + 3 is - 3 so our solution can be found by subtracting 3 from both sides, like this: g + 3 = 12 g + 3 - 3 = 12 - 3 g = 9
• Question 3

Can you solve the equation below?

7d = 56

Write the value of d as a number below.

EDDIE SAYS
Remember if there is a number right before a letter, this means that the number should be multiplied by that letter. So here, 7d = d × 7 The inverse of × 7 is ÷ 7. 7d = 56 7d ÷​ 7 = 56 ÷​ 7 d = 8
• Question 4

Solve the equation below.

z + 37 = 56

EDDIE SAYS
Let's go through the phases outlined in the Introduction. Always remember the scales - what we do to one side, we must do to the other too! z + 37 = 56 We need to subtract 37 from the right-hand side to get z, so do this to the left too! z + 37 - 37 = 56 - 37 z = 19
• Question 5

Can you match each of the equations below to their correct solution?

## 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 How did you get on with those?
• Question 6

Can you match each of the equations below to their correct solution?

## 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 that in an exam you will be given marks for showing your working, so this is a useful skill to practise. Let's work through them together. 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 an equation.

Which of the equations below has this solution?

p + 8 = 16
16 ÷ p = 2
EDDIE SAYS
We can check each equation by replacing the p with 8 and seeing if we reach 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 these are correct when p = 8. Did you get them both here?
• Question 8

x = - 4 is the solution to an equation.

Which of the equations below has this solution?

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 that a double minus makes a sneaky plus!) So this time there were three correct answers. How did you do?
• Question 9

Can you match each equation below to its correct solution?

EDDIE SAYS
Lets work out each equation to see which solution matches which. 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 Did you match those equations and solutions accurately?
• Question 10

Solve the equation below:

27 - x = 74

EDDIE SAYS
This last one is tricky, as the x is subtracted from 27, not the other way round. So it's not the same as 27 - x. Let's start by subtracting 27 from both sides. 27 - x = 74 27 - x - 27 = 74 - 27 -x = 57 Now we still have the negative sign in front 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 Hopefully you are feeling more confident now? Remember to always write down your working to earn marks in your exam, even if you make a slip and get the wrong answer.
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