Equations & Brackets.

You are now going to solve more complex equations by combining together two ideas that you have seen already . Try the following questions to make sure you are ready:

Idea 1:

Solve the equation

3x – 6 = 18

Solution :

x = 8

Idea 2 :

Multiply out the bracket

3 ( 2x – 4 )

Solution :

6x – 12

We are now going to combine these two ideas together to solve the equations on the following pages.

Solving Equations.Example 1 .

Solve the equation :

2 ( x + 4 ) = 14

Solution.

2( x + 4 ) = 14 Multiply out the bracket first.

2x + 8 = 14 Subtract 8 from both sides.

2x = 6 Divide both sides by 2 .

x = 3 Hint: check the solution by substituting x = 3 into the original equation.

Example 2 .

Solve Solve the equation :

2 ( 3x + 2 ) = 28

Solution:

2( 3x + 2 ) = 28

What should you do first ?

Multiply out the bracket.

6x + 4 = 28 What comes next ?

Subtract 4 from each side.6x = 24

What comes next ?

Divide each side by 6.

x = 4

Check your answer by putting x = 4 back into the bracket.

Example 3 .

Solve the equation :

5( x – 3 ) = 20

Solution.

5 ( x – 3 ) = 20 What does 5 times –3 equal.

-155x – 15 = 20

What must you do to both sides?

Add 15

5x = 35

x = 7

Check the answer.

What Goes In The Box 1 ?Solve the following equations:

(1) 2 ( x + 4 ) = 14

(2) 3 ( 2x + 5 ) = 27

(3) 5 ( 2x + 6 ) = 100

(4) 4 ( 3x – 5 ) = 40

(5) 7 ( 2 x – 6 ) = 28

(6) 3 ( 4 + 2x ) = 30

x = 3

x = 2

x = 7

x = 5

x = 5

x = 3