 # Solve Equations with Brackets (1)

In this worksheet, students solve equations with brackets. Key stage:

Curriculum topic:

Curriculum subtopic:

Difficulty level:   ### 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

5(b + 3) = 35

Multiply out the brackets.

5b + 15 = 35

Subtract 15 from both sides.

5b + 15 - 15 = 35 - 15

Simplify

5b = 20

Divide both sides by 5

5b ÷ 5 = 20 ÷ 5

Simplify

b = 4

Solve for a:

2(a + 4) = 38

a = 17

a = 19

a = 15

Solve for a:

3(a - 4) = -3

a = 27

a = -⅓

a = 3

Solve for a:

2(4a + 1) = 34

a = 4

a = -4

a = 28

Solve for a:

2(2a - 1) = -22

a = -5

a = 24

a = -6

Solve for a:

3(a + 3) = 27

a = 9

a = 2

a = 6

Solve for a:

5(a - 4)  = 55

a = 15

a = 3

a = 59

Solve for a:

3(2 - a) = 9

a = 8

a = -2

a = -1

Solve for a:

10(2a + 3) = 130

a = -6

a = 18

a = 5

Solve for a:

5(3 - a) = 20

a = -5

a = -1

a = 1

Solve for a:

-5(3 - a) = -20

a = -1

a = ½

a = 1

• Question 1

Solve for a:

2(a + 4) = 38

a = 15
EDDIE SAYS

Multiply out the brackets.

2a + 8 = 38

Subtract 8 from both sides.

2a + 8 - 8 = 38 - 8

Simplify

2a = 30

Divide both sides by 2

2a ÷ 2 = 30 ÷ 2

Solve for a

a = 15

• Question 2

Solve for a:

3(a - 4) = -3

a = 3
EDDIE SAYS

Multiply out the brackets.

3a - 12 = -3

Add 12 to both sides.

3a - 12 + 12 = -3 + 12

Simplify

3a = 9

Divide both sides by 3

3a ÷ 3 = 9 ÷ 3

Solve for a

a = 3

• Question 3

Solve for a:

2(4a + 1) = 34

a = 4
EDDIE SAYS

Multiply out the brackets.

8a + 2 = 34

Subtract 2 from both sides.

8a + 2 - 2 = 34 - 2

Simplify

8a = 32

Divide both sides by 8

8a ÷ 8 = 32 ÷ 8

Solve for a

a = 4

• Question 4

Solve for a:

2(2a - 1) = -22

a = -5
EDDIE SAYS

Multiply out the brackets.

4a - 2 = -22

Add 2 to both sides.

4a - 2 + 2 = -22 + 2

Simplify

4a = -20

Divide both sides by 4

4a ÷ 4 = -20 ÷ 4

Solve for a

a = -5

• Question 5

Solve for a:

3(a + 3) = 27

a = 6
EDDIE SAYS

Multiply out the brackets.

3a + 9 = 27

Subtract 9 from both sides.

3a + 9 - 9 = 27 - 9

Simplify

3a = 18

Divide both sides by 3

3a ÷ 3 = 18 ÷ 3

Solve for a

a = 6

• Question 6

Solve for a:

5(a - 4)  = 55

a = 15
EDDIE SAYS

Multiply out the brackets.

5a - 20 = 55

Add 20 to both sides.

5a - 30 + 20 = 55 + 20

Simplify

5a = 75

Divide both sides by 5

5a ÷ 5 = 75 ÷ 5

Solve for a

a = 15

• Question 7

Solve for a:

3(2 - a) = 9

a = -1
EDDIE SAYS

Multiply out the brackets.

6 - 3a = 9

subtract 6 from both sides.

6 - 3a - 6 = 9 - 6

Simplify

-3a = 3

Divide both sides by -3

-3a ÷ 3  = 3  ÷ -3

Solve for a

a = -1

• Question 8

Solve for a:

10(2a + 3) = 130

a = 5
EDDIE SAYS

Multiply out the brackets.

20a + 30 = 130

subtract 30 from both sides.

20a + 30 - 30 = 130 - 30

Simplify

20a = 100

Divide both sides by 20

20a ÷ 20  = 100 ÷ 20

Solve for a

a = 5

• Question 9

Solve for a:

5(3 - a) = 20

a = -1
EDDIE SAYS

Multiply out the brackets.

15 - 5a = 20

subtract 15 from both sides.

15 - 5a - 15 = 20 - 15

Simplify

-5a = 5

Divide both sides by -5

-5a ÷ -5  = 5 ÷ -5

Solve for a

a = -1

• Question 10

Solve for a:

-5(3 - a) = -20

a = -1
EDDIE SAYS

Multiply out the brackets.

-15 + 5a = - 20

Add 15 to both sides.

-15 + 5a + 15 = -20 + 15

Simplify

5a = -5

Divide both sides by 5

5a ÷ 5 = -5 ÷ 5

Solve for a

a = -1

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