Equations With Unknown On Both Sides

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)

Solving equations:

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? 2x4 + 1 = 4 + 5 

Solving equations:

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? 5x2 - 2 = 2x2 + 4 

On whiteboards: Solve each equation x=7 • 2x + 2 = x +9

•

3x + 1 = x +5

•

6x – 8 = 4x

•

5x + 1 = x 11

x=2 x=4 x = -3

In your books: Write each equation and solve it to find x. A) 2x – 1 = x + 3 x=4 C) 3x + 4 = x + 10 E) 5x – 6 = 2x G) 4x + 1 = x - 8 I) 2x + 3 = x + 10 K) 4x – 1 = 3x + 7 Extension:

x=3 x=2 x = -3 x=7 x=8 x=3

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 Practice

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

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

x=2

• 2 (5x + 2 ) = 5x - 1

x = -1

• 3 (x – 1) = 2 (x + 1)

x=5

• 3 (3x + 2) = 2 (x + 1)

x = -4/7

• 3 (4x – 3) = 2 (2x + 3)

x = 15/8 = 1

Extensions: 7(x – 2) = 3 (2x – 7) 3(3x - 1) = 5 (x

x=-7 x = -8

7/8

How could you check each answer?

• 2 (x + 3) = x + 7 x=1 7

means

2 (1 + 3) = 1 +

• 5 (2x - 1) = 3x + 9 2 x 4 = 8  x = 2 means +9 • 2 (5x +2 ) = 5x - 1

5 (2x2 -1) = 3x2 5x3=6+9