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Solve Two-Step Equations

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

'Solve Two-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 Equations

Difficulty level:  

Worksheet Overview

QUESTION 1 of 10

"I think of a number, multiply by 3 then add 7 and the answer is 19. What number am I thinking of?"

 

If you have completed the 'One-Step Equation' activity you will be familiar with problems like this. You will know that we can use a letter (usually x) for the unknown number then we can write the problem as an equation.

 

3x + 7 = 19

 

This equation is a bit more complex than before but we go about solving it in the same way. We 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 first remove the +7 by doing the inverse which is -7.  Then we must remove the 3 in front of the x remembering that this means 3 times x so the inverse is divide by 3. We set this out as follows:

So the solution to the equation is x = 4

 

Let's try another equation:

8x - 7 = 9

Remember the scales, what we do to one side of the equation, we must do to the other.  Remember to do the inverse of -7 before the inverse of x8.

Remember x is not always used as the unknown, examiners could use any letter, but the principle is still the same!

Here's one more example.

20 - 3w = 8

Now, this is a little trickier as the 3w is subtracted from the 20, not the other way round. This is how we do it

Remember if you divide a negative by a negative you get a positive.

Now it's over to you. All the best!

 

 

Choose the correct solution to the equation

5x +3 = 28

x = 4

x = 5

x = 6

x = 7

Here's an equation with a different letter.

6g - 1 = 23

Which of these is the correct solution?

 

g = 2

g = 3

g = 4

g = 5

Can you solve the equation 11d - 17 = 115?

 

Solve the following equation.

9z - 9 = 90

Can you match the following equations to their solutions?

Column A

Column B

2x + 4 = 18
x = 7
2x - 4 = 18
x = 11
4x - 2 = 18
x = 5
4x - 2 = 18
x = 4

Can you match each equation to its solution?

Column A

Column B

7q - 15 = -1
q = 1
7q + 15 = 8
q = 2
15q - 7 = 8
q = -2
15q + 7 = -23
q = -1

x = -1 is the solution to which of these equations. There may be more than one correct answer here.   

2x - 1 = 1

1 - 2x = 3

3x - 1 = 2

-2x - 1 = 1

3x - 2 = 1

Which of these equations has the solution x = 0.25 (you may choose more than one)?

8x - 4 = -2

4x + 9 = 10

6x + 3 = 5.5

20x - 5 = 1

16x + 19 = 21

Can you match the equations to their solutions? 

Solve the equation. 

-6 - 4x = 6

  • Question 1

Choose the correct solution to the equation

5x +3 = 28

CORRECT ANSWER
x = 5
EDDIE SAYS
Remember to get x on its own first. We have to undo +3 first and then undo x5. So here is our working: 5x +3 = 28 -3 -3 5x = 25 ÷5 ÷5 x = 5
  • Question 2

Here's an equation with a different letter.

6g - 1 = 23

Which of these is the correct solution?

 

CORRECT ANSWER
g = 4
EDDIE SAYS
How did you do? The inverse of '-1' is '+1' and the inverse of x6 is ÷6 so the solution is: 6g - 1 = 23 +1 +1 6g = 24 ÷6 ÷6 g = 4
  • Question 3

Can you solve the equation 11d - 17 = 115?

 

CORRECT ANSWER
d = 12
d=12
d =12
d= 12
12
EDDIE SAYS
This one has some bigger numbers but it's the same method. Add 17 then divide by 11. 11d - 17 = 115 +17 +17 11d = 132 ÷11 ÷11 d = 12
  • Question 4

Solve the following equation.

9z - 9 = 90

CORRECT ANSWER
EDDIE SAYS
Always remember the scales, what you do to one side, you must do to the other! And always show your working. 9z - 9 = 90 +9 +9 9z = 99 ÷9 ÷9 z = 11
  • Question 5

Can you match the following equations to their solutions?

CORRECT ANSWER

Column A

Column B

2x + 4 = 18
x = 7
2x - 4 = 18
x = 11
4x - 2 = 18
x = 4
4x - 2 = 18
x = 5
EDDIE SAYS
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. 2x + 4 = 18 → -4 then ÷2 → x = 7 2x - 4 = 18 → +4 then ÷2 → x = 11 4x + 2 = 18 → -2 then ÷4 → x = 4 4x - 2 = 18 → +2 then ÷4 → x = 5
  • Question 6

Can you match each equation to its solution?

CORRECT ANSWER

Column A

Column B

7q - 15 = -1
q = 2
7q + 15 = 8
q = -1
15q - 7 = 8
q = 1
15q + 7 = -23
q = -2
EDDIE SAYS
Did you work this out first on paper? Remember in an exam you will be given marks for showing your working. Again, here are shortened solutions. 7q - 15 = -1 → +15 then ÷7 → q = 2 7q + 15 = 8 → -15 then ÷7 → q = -1 15q - 7 = 8 → +7 then ÷15 → q = 1 15q + 7 = -23 → -7 then ÷15 → q = -2
  • Question 7

x = -1 is the solution to which of these equations. There may be more than one correct answer here.   

CORRECT ANSWER
1 - 2x = 3
-2x - 1 = 1
EDDIE SAYS
We can check each equation by replacing the x with -1 and seeing if it gives the right answer. 2x - 1 = 1 → (2 x -1) - 1 = -3 (wrong) 1 - 2x = 3 → 1 - (2 x -1) = 3 (correct) 3x - 1 = 2 → 3 x -1 - 1 = -4 (wrong) -2x - 1 = 1 → (-2 x -1) - 1 = 1 (correct) 3x - 2 = 1 → 3 x -1 - 2 = -5 (wrong) So two of them were correct. Did you get them both?
  • Question 8

Which of these equations has the solution x = 0.25 (you may choose more than one)?

CORRECT ANSWER
8x - 4 = -2
4x + 9 = 10
EDDIE SAYS
Remember, you can check each equation by replacing x with 0.25 8x - 4 = -2 → 8 x 0.25 -4 = -2 (correct) 4x + 9 = 10 → 4 x 0.25 + 9 = 10 (correct) 6x + 3 = 5.5 → 6 x 0.25 + 3 = 4.4 (wrong) 20x - 5 = 1 → 20 x 0.25 - 5 = 0 (wrong) 16x + 19 = 21 → 16 x 0.25 + 19 = 23 (wrong) So this time only the first two were correct. 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. 3a - 3 = -3 → +3 then ÷3 → a = 0 3a + 6 = -3 → -6 then ÷3 → a = -3 10a - 9 = 16 → +9 then ÷10 → a = 2.5 2a - 9 = -8 → +9 then ÷2 → a = 0.5
  • Question 10

Solve the equation. 

-6 - 4x = 6

CORRECT ANSWER
EDDIE SAYS
This last one is a tricky one as the 4x is subtracted from -6. We start by getting rid of the -6 by adding 6 to both sides. -6 - 4x = 6 +6 +6 - 4x = 12 (don't forget the '-' sign infront the 4x) ÷ -4 ÷ -4 (we divide both sides by -4 not just 4) x = -3 (dividing by -4 makes the answer negative) 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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