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Solve Two-Step Equations (including brackets)

In this worksheet, students will learn how to solve two-step linear equations which include brackets.

'Solve Two-Step Equations (including brackets)' 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 Equations

Difficulty level:  

Worksheet Overview

QUESTION 1 of 10

"I think of a number, subtract 6 then multiply by 7 and the answer is 63. What number am I thinking of?"

If you have completed 'Two-step Equations' you will be familiar with this sort of puzzle. In fact, you may be thinking this is the same, but there is an important difference in the order of operations. In this puzzle, the subtraction is performed before the multiplication and this makes a difference when we write it as an equation. Normally, in mathematics multiplication and division are performed before addition and subtraction. if we want to change this order we need to use brackets. So in order to write this puzzle as an equation with x as the unknown number we write:

7(x - 6) = 63

The x - 6 is in the bracket as this was the first step. The 7 outside the bracket means 'times 7' and was the second step. This type of equation can still be solved using the 'balancing' method where we always 'do the same to both sides' to get the x by itself. Since the x7 was performed last we 'undo' this first by ÷7, then we undo the -6 by +6.

We set out our working as follows:

So the number I thought of was 15.

Here is another equation, a little more complicated.

3(2x + 9) = 51

We need to think carefully about this one. First, the x is multiplied by 2 (2x) then 9 is added (2x + 9) and finally, it is multiplied by 3. So we need to use the inverses of these in the reverse order. Here is our working.

Now, technically this is a 3-step equation, but it uses the same method as the 2-step ones, there's just an extra line of working.

You should be getting pretty familiar with solving equations by now so no more examples. Are you ready to try some?

 

 

 

 

 

 

 

 

Choose the correct solution to the equation

2(x + 8) = 20

x = 2

x = 6

x = 14

x = 16

Here's an equation with a different letter.

3(h - 1) = 21

Which of these is the correct solution?

 

h = 6

h = 7

h = 8

h = 9

Can you solve the equation 5(t - 9) = 70?

 

Solve the following equation.

7(p + 2) = 84

Can you match the following equations to their solutions?

Column A

Column B

2(3x - 4) = -8
x = 0
3(2x - 4) = -6
x = 2
4(3x - 2) = 16
x = 1
4(2x - 3) = 12
x = 3

Can you match each equation to its solution?

Column A

Column B

3(3y - 7) = 24
y = -2
5(2y + 4) = 0
y = 4
5(4y + 3) = 95
y = 5
9(2y + 1) = 27
y = 1

x = 19 is the solution to which of these equations. There may be more than one correct answer here.   

4(2x - 27) = 48

7(x - 11) = 56

5(3x + 1) = 290

9(4x - 69) = 54

Which of these equations has the solution x = ½ (you may choose more than one)?

 

2(x + 4) = 11

4(x - 3) = -10

3(4x - 1) = 3

3(2x + 1) = 9

2(9x - 2) = 5

Can you match the equations to their solutions? 

Solve the equation

2(400 - 3x) = 326

  • Question 1

Choose the correct solution to the equation

2(x + 8) = 20

CORRECT ANSWER
x = 2
EDDIE SAYS
A straightforward one to start with. x has had 8 added then multiplied by 2. So we divide by 2 then subtract 8. Remember to set out the working correctly. 2(x + 8) = 20 ÷ 2 ÷ 2 x + 8 = 10 -8 -8 x = 2
  • Question 2

Here's an equation with a different letter.

3(h - 1) = 21

Which of these is the correct solution?

 

CORRECT ANSWER
h = 8
EDDIE SAYS
How did you do? Remember the letter is not important, it just stands for something we don't know The inverse of 'x3' is '÷ 3' and the inverse of -1 is +1. So the solution is: 3(h - 1) = 21 ÷ 3 ÷ 3 h - 1 = 7 + 1 + 1 h = 8
  • Question 3

Can you solve the equation 5(t - 9) = 70?

 

CORRECT ANSWER
t = 23
t=23
t =23
t= 23
23
EDDIE SAYS
You ought to be getting the hang of these now. To solve we need to ÷ 5 then +9. 5(t - 9) = 70 ÷ 5 ÷ 5 t - 9 = 14 +9 +9 t = 23
  • Question 4

Solve the following equation.

7(p + 2) = 84

CORRECT ANSWER
EDDIE SAYS
Don't forget to start by getting rid of the number outside the bracket. 7(p + 2) = 84 ÷ 7 ÷ 7 p + 2 = 12 -2 -2 p = 10
  • Question 5

Can you match the following equations to their solutions?

CORRECT ANSWER

Column A

Column B

2(3x - 4) = -8
x = 0
3(2x - 4) = -6
x = 1
4(3x - 2) = 16
x = 2
4(2x - 3) = 12
x = 3
EDDIE SAYS
Did you spot these are 3-step equations? There is a lot to work through here and take up a lot of space so we'll keep it brief. Here are the inverses in the correct order for each equation. 2(3x - 4) = -8 → ÷ 2 then +4 then ÷ 3 → x = 0 3(2x - 4) = -6 → ÷ 3 then +4 then ÷ 2 → x = 1 4(3x - 2) = 16 → ÷ 4 then +2 then ÷ 3 → x = 2 4(2x - 3) = 12 → ÷ 4 then +3 then ÷ 2 → x = 3 Did you get them all right?
  • Question 6

Can you match each equation to its solution?

CORRECT ANSWER

Column A

Column B

3(3y - 7) = 24
y = 5
5(2y + 4) = 0
y = -2
5(4y + 3) = 95
y = 4
9(2y + 1) = 27
y = 1
EDDIE SAYS
Some more 3-step equations. Again, here are shortened solutions. 3(3y - 7) = 24 → ÷ 3 then +7 then ÷ 3 → y = 5 5(2y + 4) = 0 → ÷ 5 then -4 then ÷ 2 → y = -2 5(4y + 3) = 95 → ÷ 5 then -3 then ÷ 4 → y = 4 9(2y + 1) = 27 → ÷ 9 then -1 then ÷ 2 → y = 1 How are you doing? Don't worry if you make mistakes, as long as you can see why you got it wrong.
  • Question 7

x = 19 is the solution to which of these equations. There may be more than one correct answer here.   

CORRECT ANSWER
7(x - 11) = 56
5(3x + 1) = 290
EDDIE SAYS
There are some big numbers here but don't be tempted to reach for a calculator! We can check each equation by replacing the x with 19 and seeing if it gives the right answer. 4(2x - 27) = 44 → 4x(2 x 19 - 27) = 4 x 11 = 44 (wrong) 7(x - 11) = 56 → 7x(19 - 11) = 7 x 8 = 56 (correct) 5(3x + 1) = 195 → 5(3 x 19 + 1) = 5 x 58 = 290 (correct) 9(4x - 69) = 54 → 9x(4 x 19 - 69) = 9 x 7 = 63 (wrong) So two of them were correct. Did you get them both?
  • Question 8

Which of these equations has the solution x = ½ (you may choose more than one)?

 

CORRECT ANSWER
4(x - 3) = -10
3(4x - 1) = 3
2(9x - 2) = 5
EDDIE SAYS
Remember, you can check each equation by replacing x with ½ 2(x + 4) = 11 → 2 x (½ + 4) = 9 (wrong) 4(x - 3) = -10 → 4 x (½ - 3) = -10 (correct) 3(4x - 1) = 3 → 3 x (4x½ - 1) = 3 x 1 = 3 (correct) 3(2x + 1) = 9 → 3 x (2x½ + 1) = 3 x 2 = 6 (wrong) 2(9x - 2) = 5 → 2 x (9x½ - 2) = 2 x 2.5 = 5 (correct) 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
Let's work out each equation to see which solution matches. 3(3n - 4) = 33 → ÷ 3 then +4 then ÷3 → n = 5 2(2n + 3) = 6 → ÷ 2 then -3 then ÷2 → n = 0 5(2n + 1) = 20 → ÷ 5 then -1 then ÷2 → n = 1.5 42 = 3(4 + 5n) → ÷ 3 then -4 then ÷5 → n = 2 Don't be put off that this last one is written 'back to front'. It's just the same as the otheres really.
  • Question 10

Solve the equation

2(400 - 3x) = 326

CORRECT ANSWER
EDDIE SAYS
This is a nasty one! There are some big numbers here but the method is still the same. 2(400 - 3x) = 326 ÷ 2 ÷ 2 400 - 3x = 163 -400 -400 -3x = -237 (dont forget the '-' infront of the 237 ÷ -3 ÷ -3 (we have to divide by -3 not just 3) x = 79 Well done, if you got this one right. And that's a whole exercise finished! Excellent!
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