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Lesson 13

Lesson 13. Booster Lesson. 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.

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Lesson 13

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  1. Lesson 13 Booster Lesson

  2. 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

  3. 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

  4. 56 a x + 8 2 7 x + 2 11 x + 5 Solving equations M13.1 Set 1 1.1 3x = 13 1.2 6C + 8 = 80 1.3 18 = 7p - 24 1.4 2(n + 4) = 72 1.5 4(d - 1) + 3(d + 4) = 57 Set 2 2.1 9x = 43 2.2 7 = 2.3 3x + 6 = 2x + 13 2.4 3(x + 2) = 4(x - 1) 2.5 = x - 2 Set 3 3.1 7x = -37 3.2 3(s - 1) - 2(s - 2) = 0 3.3 2(t + 1) - 5(t + 2) = 0 3.4 7(h + 3) = 11 3.5 =

  5. Set 1 1.1 3x = 13 1.2 6C + 8 = 80 1.3 18 = 7p - 24 1.4 2(n + 4) = 72 1.5 4(d - 1) + 3(d + 4) = 57 1.1 3x = 13 Divide both sides by 3 x = 4.3333… Take 8 from both sides 1.2 6c + 8 = 80 Divide both sides by 6 6c = 72 c = 12 1.3 18 = 7p - 24 Add 24 to both sides 42 = 7p Divide both sides by 7 6 = p 1.4 2( n + 4) = 72 Divide by 2 on both sides Take 4 from both sides n + 4 = 36 n = 32 1.5 4( d – 1 ) + 3 (d + 4) = 57 Multiply out brackets 4d – 4 + 3d + 12 = 57 Collect like terms 7d + 8 = 57 Take 8 Divide by 7 7d = 49 d = 7 Check your solution

  6. Set 2 2.1 9x = 43 2.2 7 = 56 a 2.3 3x + 6 = 2x + 13 2.4 3(x + 2) = 4(x - 1) 2.5 x + 8 = x – 2 2 2.1 9x = 43 Divide both sides by 9 x = 4.7777.. 2.2 7 = 56 a Multiply both sides by a Check yoursolution Divide both sides by 7 7a = 56 a = 8 2.3 3x + 6 = 2x + 13 Take 6 from both sides 3x = 2x + 7 Take 2x from both sides x = 7 Multiply out brackets 2.4 3 ( x + 2 ) = 4 ( x – 1) 3x + 6 = 4x - 4 Take 6 from both sides 3x = 4x - 10 Take 4x from both sides -x = - 10 x = 10 Multiply both sides by 2 2.5 x + 8 = x – 2 2 x + 8 = 2x - 4 Take x from both sides 8 = x - 4 Add 4 to both sides 12 = x

  7. Set 3 3.1 7x = -37 3.2 3(s - 1) - 2(s - 2) = 0 3.3 2(t + 1) - 5(t + 2) = 0 3.4 7(h + 3) = 11 3.5 7 = 11 x + 2 x + 5 Check your solution Divide both sides by 7 3.1 7x = - 37 x = - 5.285… 3.2 3( s – 1 ) – 2 (s – 2 ) = 0 Multiply out brackets 3s – 3 – 2s + 4 = 0 Collect like terms s + 1 = 0 Take 1 from both sides s = - 1 3.3 2( t+ 1) – 5(t + 2) = 0 Multiply out brackets 2t + 2 – 5t – 10 = 0 Collect like terms - 3t - 8 = 0 Add 3t to both sides Divide by 3 - 8 = 3t - 2.666.. = t 3.4 7( h + 3 ) = 11 Multiply out brackets Take 21 from both sides 7h + 21 = 11 Divide by 7 7h = - 10 h = - 1.428..

  8. 3.5 7 = 11 x + 2 x + 5 Cross multiply Multiply out brackets 7( x + 5 ) = 11( x + 2) Take 22 7x + 35 = 11x + 22 Take 7x 7x + 13 = 11x Divide by 4 13 = 4x Check your solution 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 Take 2x from both sides 2x = 6 Divide by 2 x = 3 Check the solution; Multiply 3 by 4 then subtract 5 Answer 7 check Answer 7 Multiply 3 by 2 and add 1

  9. 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?

  10. Objectives – how have we done? • Construct simple linear equations • Solve simple linear equations • Check solutions by substituting

  11. Thank you for your attention

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