 # Solve Equations (3)

In this worksheet, students solve two-stage equations with brackets. Key stage:  KS 3

Curriculum topic:   Algebra

Curriculum subtopic:   Understand Expressions, Equations, Inequalities, Terms and Factors

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.

Example

Solve  4(2b + 1) = 3(8 + b)

Multiply out the brackets

8b + 4 = 24 + 3b

Subtract 4 from both sides.

8b + 4 - 4 = 24 + 3b - 4

Simplify

8b = 20 + 3b

Subtract 3b from both sides.

8b - 3b = 20 + 8b - 3b

Simplify

5b = 20

Divide both sides by 5

5b ÷ 5 = 20 ÷ 5

Simplify

b = 4

Solve for a:

5(3a - 1) = -20

a = 3

a = -1

a = 4

Solve for a:

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

a = -8

a = 1

a = 4

Solve for a:

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

a = -4

a = 4

a = 20

Solve for a:

2(13a - 1) = 22(a - 1)

a = -3

a = -4

a = -5

Solve for a:

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

a = -2

a = 2

a = 8

Solve for a:

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

a = -3

a = 2

a = -2

Solve for a:

4(a + 5) = 3(2a + 10)

a = 5

a = -20

a = -5

Solve for a:

5(a - 20) = -2(2a + 5)

a = 10

a = 5

a = 0

Solve for a:

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

a = -1

a = -5

a = 1

Solve for a:

3(2a + 3) = -2(2a + 7)

a = -2

a = -2.3

a = -½

• Question 1

Solve for a:

5(3a - 1) = -20

a = -1
• Question 2

Solve for a:

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

a = -8
• Question 3

Solve for a:

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

a = 20
• Question 4

Solve for a:

2(13a - 1) = 22(a - 1)

a = -5
• Question 5

Solve for a:

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

a = 8
• Question 6

Solve for a:

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

a = -3
• Question 7

Solve for a:

4(a + 5) = 3(2a + 10)

a = -5
• Question 8

Solve for a:

5(a - 20) = -2(2a + 5)

a = 10
• Question 9

Solve for a:

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

a = -5
• Question 10

Solve for a:

3(2a + 3) = -2(2a + 7)

a = -2.3
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