1. Equations with the unknown on both sides.
Lesson Objective:
An equation is like a set of scales.
To keep it balanced, whatever you
do to one side you must do to the other.
Use this idea to solve equations like:
3x + 1 = x + 7
2 (3x + 1) = 3 (x – 2)

2. Solving equations: 2x + 1 = x + 5 Subtract x from each side x + 1 = 5
Only want ‘x’ on one side
2x + 1 = x + 5
Subtract x from each side
x + 1 = 5
Subtract 1 from each side
x = 4
Check your answer. Does the equation balance?
2x = P

3. Solving equations: 5x - 2 = 2x + 4 Subtract 2x from each side
Only want ‘x’ on one side
5x - 2 = 2x + 4
Subtract 2x from each side
3x - 2 = 4
Add 2 to each side
3x = 6
Divide each side by 3
x = 2
Check your answer. Does the equation balance?
5x = 2x P

4. On whiteboards: Solve each equation
2x + 2 = x + 9
3x + 1 = x + 5
6x – 8 = 4x
5x + 1 = x - 11
x = 7
x = 2
x = 4
x = -3

5. In your books: Write each equation and solve it to find x.
2x – 1 = x + 3
3x + 4 = x + 10
5x – 6 = 2x
4x + 1 = x - 8
2x + 3 = x + 10
4x – 1 = 3x + 7
Extension:
2x - 6 = - 3x + 9
x = 4
x = 3
x = 2
x = -3
x = 7
x = 8

6. Solving equations with brackets:
2 (x + 3) = x + 11
Multiply out the bracket
2x + 6 = x + 11
Subtract x from each side
x + 6 = 11
Subtract 6 from each side
x = 5

7. Solving equations with brackets on both sides:
2 (3x – 1 ) = 3 (x + 2)
Multiply out the brackets
6x - 2 = 3x + 6
Subtract 3x from each side
3x -2 = + 6
Add 2 to each side
3x = 8
Divide each side by 3
x = 8/3 = 2 2/3

8. In your books: Write each equation and solve it to find x.
2 (x + 3) = x + 7
5 (2x - 1) = 3x + 9
2 (5x + 2 ) = 5x - 1
3 (x – 1) = 2 (x + 1)
3 (3x + 2) = 2 (x + 1)
3 (4x – 3) = 2 (2x + 3)
Extensions: 7(x – 2) = 3 (2x – 7)
3(3x - 1) = 5 (x – 7)

9. How could you check each answer?
2 (x + 3) = x + 7
5 (2x - 1) = 3x + 9
2 (5x + 2 ) = 5x - 1
x = 1 means 2 (1 + 3) = 1 + 7
2 x 4 = 8 P
x = 2 means 5 (2x2 -1) = 3x2 + 9
5 x 3 = P
x = -1 means 2 (5 x-1 +2) = 5 x-1 -1
2 (-5 + 2) = -5 -1
2 x -3 = P