1. Equations & Brackets.

2. 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.

3. Solving Equations. Example 1. Solve the equation : 2 ( x + 4 ) = 14 Solution. 2( x + 4 ) = 14Multiply out the bracket first. 2x + 8 = 14 Subtract 8 from both sides. 2x = 6 Divide both sides by 2. x = 3Hint: check the solution by substituting x = 3 into the original equation.

4. 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.

5. 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.

6. 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 = 3