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Booster Lesson Lesson 13 Objectives – what you should be able to do by the end of the lesson • Construct simple linear equations • Solve simple linear equations • Check solutions by substituting John is y years old. Jane is x years old. John is 8 years older than Jane. Can you write this as an algebraic equation? y=x+8 In one’s year time, what will John and Jane’s age be? Can you write another algebraic equation? y+1=x+9 Can you add 3 to both sides? y + 4 = x + 12 Can you take away 4 from both sides? y=x+8 John is also twice the age of Jane. Can you write this as an equation? y = x + 8 = 2x Solving equations M13.1 Set 1 1.1 1.2 1.3 1.4 1.5 3x = 13 6C + 8 = 80 18 = 7p - 24 2(n + 4) = 72 4(d - 1) + 3(d + 4) = 57 Set 2 2.1 2.2 2.3 2.4 2.5 9x = 43 7 = 56 a 3x + 6 = 2x + 13 3(x + 2) = 4(x - 1) x+8 =x-2 2 Set 3 3.1 3.2 3.3 3.4 3.5 7x = -37 3(s - 1) - 2(s - 2) = 0 2(t + 1) - 5(t + 2) = 0 7(h + 3) = 11 7 = 11 x+2 x+5 Set 1 1.1 1.1 1.2 1.3 1.4 1.5 3x = 13 3x = 13 6C + 8 = 80 18 = 7p - 24 2(n + 4) = 72 4(d - 1) + 3(d + 4) = 57 Divide both sides by 3 x = 4.3333… 1.2 6c + 8 = 80 6c = 72 c = 12 Take 8 from both sides Divide both sides by 6 1.3 18 = 7p - 24 42 = 7p Add 24 to both sides Divide both sides by 7 6=p 1.4 2( n + 4) = 72 n + 4 = 36 n = 32 Divide by 2 on both sides Take 4 from both sides 1.5 4( d – 1 ) + 3 (d + 4) = 57 4d – 4 + 3d + 12 = 57 7d + 8 = 57 7d = 49 d=7 Multiply out brackets Collect like terms Take 8 Divide by 7 Set 2 2.1 2.2 2.3 2.4 2.5 2.1 9x = 43 9x = 43 7 = 56 a 3x + 6 = 2x + 13 3(x + 2) = 4(x - 1) x+8 =x–2 2 Divide both sides by 9 x = 4.7777.. 2.2 7 = 56 Multiply both sides by a a 7a = 56 Divide both sides by 7 a=8 2.3 3x + 6 = 2x + 13 3x = 2x + 7 Take 6 from both sides Take 2x from both sides x=7 2.4 3 ( x + 2 ) = 4 ( x – 1) 3x + 6 = 4x - 4 3x = 4x - 10 -x = - 10 2.5 Multiply out brackets Take 6 from both sides Take 4x from both sides x = 10 x+8=x–2 Multiply both sides by 2 2 x + 8 = 2x - 4 Take x from both sides 8=x-4 12 = x Add 4 to both sides Set 3 3.1 3.1 3.2 3.3 3.4 3.5 7x = -37 3(s - 1) - 2(s - 2) = 0 2(t + 1) - 5(t + 2) = 0 7(h + 3) = 11 7 = 11 x+2 x+5 Divide both sides by 7 7x = - 37 x = - 5.285… 3.2 3( s – 1 ) – 2 (s – 2 ) = 0 3s – 3 – 2s + 4 = 0 Multiply out brackets Collect like terms s + 1 = 0 Take 1 from both sides s=-1 3.3 2( t+ 1) – 5(t + 2) = 0 2t + 2 – 5t – 10 = 0 - 3t - 8 = 0 - 8 = 3t Multiply out brackets Collect like terms Add 3t to both sides Divide by 3 - 2.666.. = t 3.4 7( h + 3 ) = 11 Multiply out brackets Take 21 from both sides Divide by 7 7h + 21 = 11 7h = - 10 h = - 1.428.. 3.5 7 x+2 = 11 x+5 Cross multiply 7( x + 5 ) = 11( x + 2) 7x + 35 = 11x + 22 7x + 13 = 11x 13 = 4x Multiply out brackets Take 22 Take 7x Divide by 4 3.25 = x A problem to solve: What is my number? Multiplying my number by 4 and then subtracting 5 gives the same answer as multiplying my number by 2 and then adding 1. Use a letter to represent my number and write an equation 4x – 5 = 2x + 1 Add 5 to both sides Solve the equation. 4x = 2x + 6 2x = 6 Take 2x from both sides Divide by 2 x=3 Check the solution; Multiply 3 by 4 then subtract 5 Answer 7 Answer 7 Multiply 3 by 2 and add 1 check Number puzzles Two number multiply together to make 24. They add together to make 11. What are my numbers? How did you work it out? Two numbers multiply together to make -15. They add together to make 2. What are my numbers? How did you work it out? Two numbers multiply together to make – 15. They add together to make – 2. What are my numbers? How did you work it out? Two numbers multiply together to make 8. they add together to make – 6. What are my numbers? How did you work it out? Objectives – how have we done? • Construct simple linear equations • Solve simple linear equations • Check solutions by substituting Thank you for your attention