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Solve Equations with Brackets (2)

In this worksheet, students solve equations with two sets of brackets.

'Solve Equations with Brackets (2)' worksheet

Key stage:  KS 3

Curriculum topic:  Algebra

Curriculum subtopic:  Solve Linear Equations (One Variable)

Difficulty level:  

down

Worksheet Overview

QUESTION 1 of 10

When we solve algebraic equations, our aim is to end up with one letter on one side of the equals sign and one number on the other.  This is the solution.

We do this by using inverse operations to undo things that get in the way, but remember that we must do the same thing to both sides.

When brackets are involved, we multiply out the brackets first.

 

Example

7(b + 3) - 2(b - 3) = 47

 

Answer

Multiply out each set of brackets.

7b + 21 - 2b + 6 = 47

Simplify by collecting like terms.

5b + 27 = 47

Subtract 27 from both sides.

5b + 27 - 27 = 47 - 27

Simplify

5b = 20

Divide both sides by 5

5b ÷ 5 = 20 ÷ 5

Simplify

b = 4

Solve for a:

2(a + 4)  + 3(a + 1) = 46

 

a = 5

a = 9

a = 7

Solve for a:

3(a - 1) + 2(a + 1) = 9

 

a = -⅓

a = 2

a = 3

Solve for a:

2(4a + 1) + 3(a - 1) = 43

 

a = -4

a = 4

a = 2

Solve for a:

2(2a - 1) - 3(a + 1) = 1

 

a = 6

a = 4

a = -5

Solve for a:

3(a + 3) - 2(a + 3) = 27

 

a = 24

a = 2

a = 9

Solve for a:

5(a - 4) + 3(2a - 1) = 76

 

a = 9

a = 3

a = 15

Solve for a:

3(2 - a) + 5(2a - 3) = -23

 

a = -1

a = -2

a = 8

Solve for a:

10(2a + 3) - 4(a - 2) = 134

 

a = 5

a = 18

a = 6

Solve for a:

5(3 - a) - 2 (4 - 2a) = 8

 

a = -1

a = -5

a = 1

Solve for a:

-5(3 - a) + 3(a - 2) = -5

 

a = ½

a = -1

a = 2

  • Question 1

Solve for a:

2(a + 4)  + 3(a + 1) = 46

 

CORRECT ANSWER
a = 7
  • Question 2

Solve for a:

3(a - 1) + 2(a + 1) = 9

 

CORRECT ANSWER
a = 2
  • Question 3

Solve for a:

2(4a + 1) + 3(a - 1) = 43

 

CORRECT ANSWER
a = 4
  • Question 4

Solve for a:

2(2a - 1) - 3(a + 1) = 1

 

CORRECT ANSWER
a = 6
  • Question 5

Solve for a:

3(a + 3) - 2(a + 3) = 27

 

CORRECT ANSWER
a = 24
  • Question 6

Solve for a:

5(a - 4) + 3(2a - 1) = 76

 

CORRECT ANSWER
a = 9
  • Question 7

Solve for a:

3(2 - a) + 5(2a - 3) = -23

 

CORRECT ANSWER
a = -2
  • Question 8

Solve for a:

10(2a + 3) - 4(a - 2) = 134

 

CORRECT ANSWER
a = 6
  • Question 9

Solve for a:

5(3 - a) - 2 (4 - 2a) = 8

 

CORRECT ANSWER
a = -1
  • Question 10

Solve for a:

-5(3 - a) + 3(a - 2) = -5

 

CORRECT ANSWER
a = 2
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