# Simplify and Solve Equations (2)

In this worksheet, students simplify like terms before solving simple one-stage equations.

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 simplifying like terms if we can and then using inverse operations to undo things that get in the way, but remember that we must do the same thing to both sides.

Example

7b - 2b + 5b= -20

Answer

Simplify the left hand side by combining like terms

10b = -20

Divide both sides by 10

10b ÷ 10 = -20 ÷ 10

Simplify

b = -2

Solve for a:

7a - 3a - a = 12

a = 3

a = 4

12

Solve for a:

4a + a + 5a = 25

a = 15

a = -11

a = 2.5

Solve for a:

5a + 2a - 4a = 42

a = 14

a = 6

a = 28

Solve for a:

6a + 5a - 2a = 27

a = 3

a = 33

a = 2

Solve for a:

5a - 4a + 22a = 0

a = 0

a = -23

a = 23

Solve for a:

10a - 2a + 7a = 45

a = 6

a = -6

a = 3

Solve for a:

-a + 11a - 12a + a = 18

a = -18

a = 6

a = 18

Solve for a:

3a - 6a + 5a - 4a = 18

a = 16

a = -9

a = -6

Solve for a:

2a - a + 5a - a = -15

a = -10

a = -13

a = -3

Solve for a:

-10a + 25a + 5a - 10a = -40

a = 15

a = -15

a = -4

• Question 1

Solve for a:

7a - 3a - a = 12

CORRECT ANSWER
a = 4
• Question 2

Solve for a:

4a + a + 5a = 25

CORRECT ANSWER
a = 2.5
• Question 3

Solve for a:

5a + 2a - 4a = 42

CORRECT ANSWER
a = 14
• Question 4

Solve for a:

6a + 5a - 2a = 27

CORRECT ANSWER
a = 3
• Question 5

Solve for a:

5a - 4a + 22a = 0

CORRECT ANSWER
a = 0
• Question 6

Solve for a:

10a - 2a + 7a = 45

CORRECT ANSWER
a = 3
• Question 7

Solve for a:

-a + 11a - 12a + a = 18

CORRECT ANSWER
a = -18
• Question 8

Solve for a:

3a - 6a + 5a - 4a = 18

CORRECT ANSWER
a = -9
• Question 9

Solve for a:

2a - a + 5a - a = -15

CORRECT ANSWER
a = -3
• Question 10

Solve for a:

-10a + 25a + 5a - 10a = -40

CORRECT ANSWER
a = -4
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