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Refresher Solving Equations x x + 5 Remember: 1. We have previously solved simple equations like the one shown and we looked at the analogy of scales in which both sides are balanced. 2 x + 5 = x + 10 x + 5 = 10 x = 5 2. We have previously expanded single brackets as shown below. 5(2x - 3) means 5 x (2x - 3) = 10x We are familiar with the rules for signs when multiplying. + x + = + + x - = - - x + = - - x - = +- x - = + Unlike signs give a negative We now need to know that the same rules apply for division.

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Ex Qs 2 Brackets Solving Equations Example Questions With Brackets 2( x + 1) = x + 5 Example Question 1: solve 2 x + 2 = x + 5 x + 2 = 5 x = 3 3 x - 3 = 2 x + 14 x - 3 = 14 x = 17 3( x - 1) = 2( x + 7) Example Question 2: solve 3( x - 2) - 2( x + 1) = 5 Example Question 3: solve 3 x x - 2 = 5 x - 8 = 5 x = 13 7( x - 2) - 4 = 2( x + 2) Example Question 4: solve 7 x = 2 x x - 18 = 2 x x - 18 = 4 5 x = 22 x = 4.4

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Questions 2 Solving Equations Solve the following equations (a) 8( x + 1) = 2( x + 16) (c) 6( x - 5) = 5( x - 4) (d) 3( x + 2) = 2( x - 1) (b) 10( x + 1) = 7( x + 4) (e) 7( x - 2) - 3 = 2( x + 2) (f) 3( x + 1) + 2( x + 2) = 10 (g) 5( x - 3) + 3( x + 2) = 7 x (h) 2 x - 3( x + 2) = 2 x + 1

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Worksheets Worksheet 1 (a) 6 x + 8 = 2 x - 12 (b) 5 x - 4 = x (c) x = 12 - x (d) x = 7 + x (e) 2 x - 7 = x (f) 9 x + 25 = 5 + x (g) 7 x + 8 = x (a) 8( x + 1) = 2( x + 16) (c) 6( x - 5) = 5( x - 4) (d) 3( x + 2) = 2( x - 1) (b) 10( x + 1) = 7( x + 4) (e) 7( x - 2) - 3 = 2( x + 2) (f) 3( x + 1) + 2( x + 2) = 10 (g) 5( x - 3) + 3( x + 2) = 7 x (h) 2 x - 3( x + 2) = 2 x + 1 Questions 1 Questions 2 (a) 6 x + 8 = 2 x - 12 (b) 5 x - 4 = x (c) x = 12 - x (d) x = 7 + x (e) 2 x - 7 = x (f) 9 x + 25 = 5 + x (g) 7 x + 8 = x (a) 8( x + 1) = 2( x + 16) (c) 6( x - 5) = 5( x - 4) (d) 3( x + 2) = 2( x - 1) (b) 10( x + 1) = 7( x + 4) (e) 7( x - 2) - 3 = 2( x + 2) (f) 3( x + 1) + 2( x + 2) = 10 (g) 5( x - 3) + 3( x + 2) = 7 x (h) 2 x - 3( x + 2) = 2 x + 1 Questions 1 Questions 2

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