# Solve Equations with Brackets (2)

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

Key stage:  KS 3

Curriculum topic:   Algebra

Curriculum subtopic:   Solve Linear Equations (One Variable)

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

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

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

a = 7
EDDIE SAYS
Multiply out each bracket 2a + 8 + 3a + 3 = 46 Collect the alike terms 5a + 11 = 46 Solve as you would a normal linear equation a=7
• Question 2

Solve for a:

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

a = 2
EDDIE SAYS
Multiply out each bracket 3a - 3 + 2a + 2 = 9 Collect the alike terms 5a - 1 = 9 Solve as you would a normal linear equation a=2
• Question 3

Solve for a:

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

a = 4
EDDIE SAYS
Multiply out each bracket 8a + 2 + 3a - 3 = 43 Collect the alike terms 8a + 3a = 43 - 2 + 3 Solve as you would a normal linear equation 11a = 44 a=4
• Question 4

Solve for a:

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

a = 6
EDDIE SAYS
Multiply out each bracket 4a- 2 -3a -3 =1 Collect the alike terms a - 5 = 1 Solve as you would a normal linear equation a=6
• Question 5

Solve for a:

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

a = 24
EDDIE SAYS
Multiply out each bracket 3a + 9 - 2a - 6 = 27 Collect the alike terms a + 3 = 27 Solve as you would a normal linear equation a = 24
• Question 6

Solve for a:

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

a = 9
EDDIE SAYS
Multiply out each bracket 5a - 20 + 6a - 3 = 76 Collect the alike terms 11a - 23 = 76 Solve as you would a normal linear equation a = 9
• Question 7

Solve for a:

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

a = -2
EDDIE SAYS
Multiply out each bracket 6 - 3a + 10a -15 = -23 Collect the alike terms 7a - 9 = -23 Solve as you would a normal linear equation a = -2
• Question 8

Solve for a:

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

a = 6
EDDIE SAYS
Multiply out each bracket 20a + 30 - 4a + 8 = 134 Collect the alike terms 16a + 38 = 134 Solve as you would a normal linear equation a=6
• Question 9

Solve for a:

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

a = -1
EDDIE SAYS
Multiply out each bracket 15 - 5a - 8 + 4a = 8 Collect the alike terms -a + 7 = 8 Solve as you would a normal linear equation a = -1
• Question 10

Solve for a:

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

a = 2
EDDIE SAYS
Multiply out each bracket -15 + 5a + 3a - 6 = -5 Collect the alike terms 8a - 21 = -5 Solve as you would a normal linear equation a = 2
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