# Solve Equations

In this worksheet, students solve multi-stage equations.

Key stage:  KS 4

Curriculum topic:  Algebra

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

-8b + 3 = 23 + 3b

Subtract 3 from both sides.

-8b + 3 - 3 = 23 + 3b - 3

Simplify

-8b = 20 + 3b

Subtract 3b from both sides.

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

Simplify

-11b = 20

Divide both sides by -11

-11b ÷ -11 = 20 ÷ -11

Simplify

b = -20/11

Solve for a:

-5a + 40 = 46 + 2a

a = 30

a = -6/7

a = 49/3

Solve for a:

-13a - 4 - a = 8

a = -⅓

a = -6/7

a = 7/6

Solve for a:

7a + 8 - a = -24 + a

a = -6.4

a = 4

a = -32

Solve for a:

26a - 2 = -22a - 22

a = -1/2

a = -1/3

a = -5/12

Solve for a:

-22a + 4 = -6 - 4a

a = -2

a = 2/9

a = 5/9

Solve for a:

-5a - 9 = 5 - 2a

a = -14/3

a = 14/3

a = -2

Solve for a:

-5 - 4a = 90 + 2a - a

a = 84

a = -21/5

a = -19

Solve for a:

7 -4a - 2 = 197 - 7a

a = 64

a = 54

a = -64

Solve for a:

4 - 15 - 6a = 20 - 15a

a = 9/13

a = -5

a = 31/9

Solve for a:

10a -16 - 2a = a -21 + 3a

a = -1.25

a = -0.8

a = 4/5

• Question 1

Solve for a:

-5a + 40 = 46 + 2a

a = -6/7
• Question 2

Solve for a:

-13a - 4 - a = 8

a = -6/7
• Question 3

Solve for a:

7a + 8 - a = -24 + a

a = -6.4
• Question 4

Solve for a:

26a - 2 = -22a - 22

a = -5/12
• Question 5

Solve for a:

-22a + 4 = -6 - 4a

a = 5/9
• Question 6

Solve for a:

-5a - 9 = 5 - 2a

a = -14/3
• Question 7

Solve for a:

-5 - 4a = 90 + 2a - a

a = -19
• Question 8

Solve for a:

7 -4a - 2 = 197 - 7a

a = 64
• Question 9

Solve for a:

4 - 15 - 6a = 20 - 15a

a = 31/9
• Question 10

Solve for a:

10a -16 - 2a = a -21 + 3a