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Equations & Inequalities

Equations & Inequalities. Revision of Level 2 Algebra. Harder Equations. Equations with Brackets. www.mathsrevision.com. Equations with Fractions. Harder Fractions. Solving Inequalities. Starter Questions. www.mathsrevision.com. Revision of Level 2. Equations & Inequalities.

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Equations & Inequalities

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  1. Equations & Inequalities Revision of Level 2 Algebra Harder Equations Equations with Brackets www.mathsrevision.com Equations with Fractions Harder Fractions Solving Inequalities Created by Mr. Lafferty Maths Dept.

  2. Starter Questions www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

  3. Revision of Level 2 Equations & Inequalities Learning Intention Success Criteria • To revise Level 2 • using the rule • ‘Balancing Method’ • 1. Understand the process of the • ‘Balancing Method’ • 2. Solving simple algebraic equations. www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

  4. Kirsty goes to the shops every week to buy some potatoes. She always buys the same total weight. One week she buys 2 large bags and 1 small bag. The following week she buys 1 large bag and 3 small bags. Balancing Method If a small bags weighs 4 kgs. How much does a large bag weigh? 4 www.mathsrevision.com 4 4 4 What instrument measures balance How can we go about solving this using balance ? Created by Mr Lafferty Maths Dept

  5. Take a small bag away from each side. Balancing Method 4 4 4 4 Take a big bag away from each side. www.mathsrevision.com We can see that a big bag is equal to 4 + 4 = 8 kg Created by Mr Lafferty Maths Dept

  6. What symbol should we use for the scales ? Lets solve it using maths. Balancing Method 4 P P P Let P be the weigh of a big bag. 4 4 4 We know that a small bag = 4 www.mathsrevision.com Subtract 4 from each side 2P + 4 P + 12 = -4 -4 Subtract P from each side 2P = P + 8 -P -P P = 8 Created by Mr Lafferty Maths Dept

  7. Group of 5 adults and 3 children go to the local swimming. Another group of 3 adults and 8 children also go swimming. The total cost for each group is the same. A child’s ticket costs £2. Balancing Method If a child’s ticket costs £2. How much for an adult ticket ? www.mathsrevision.com 2 2 2 2 a 2 a 2 2 a 2 Let a be the price of an adult ticket. 2 a a 2 a a 2 a We know that a child price = £2 Created by Mr Lafferty Maths Dept

  8. Subtract 3a from each side Subtract 6 from each side For balance we have Balancing Method 2 a 2 a a 5a + 6 3a + 16 2 = a 2 2 2 -6 -6 a a 2 2 2 2 1 a 2 5a = 3a + 10 a -3a -3a Divide each side by 2 www.mathsrevision.com 2a = 10 a = 5 Adult ticket price is £5 Created by Mr Lafferty Maths Dept

  9. Balancing Method It would be far too time consuming to draw out the balancing scales each time. We will now review how to use the rules for solving equations. www.mathsrevision.com Created by Mr Lafferty Maths Dept

  10. Equations & Inequalities Revision of Level 2 MTH 3-15a MTH 4-15a Reminder ! The Balancing Method Examples x – 5 = 11 x + 8 = 37 www.mathsrevision.com + 5 + 5 - 8 - 8 x = 16 x = 29 Created by Mr. Lafferty Maths Dept.

  11. Equations & Inequalities Revision of Level 2 MTH 3-15a MTH 4-15a Reminder ! The Balancing Method Examples 6x = 72 2x = 11 www.mathsrevision.com (÷ 6) (÷ 2) x = 12 x = 5.5 Created by Mr. Lafferty Maths Dept.

  12. Equations & Inequalities Revision of Level 2 MTH 3-15a MTH 4-15a Examples 4x – 2 = 34 2x + 9 = 31 + 2 + 2 + 9 + 9 4x = 36 2x = 22 www.mathsrevision.com (÷ 4) (÷ 2) x = 9 x = 11 Created by Mr. Lafferty Maths Dept.

  13. Equations & Inequalities Revision of Level 2 MTH 3-15a MTH 4-15a Now try Exercise 1 Ch43 (page 171) www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

  14. 100o 60o Starter Questions 2x 6x www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

  15. Harder Equations Equations & Inequalities Learning Intention Success Criteria • Apply balancing method to solve equations with more than one x term. • 1. We are learning how to apply balancing method to solve harder equations. www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

  16. Each group has 2 minutes come up with a method for solving this type of equation Equations & Inequalities Harder Equations MTH 3-15a MTH 4-15a Examples 3x + 2 = x + 10 4x - 5 = 2x - 25 - 2 - 2 + 5 + 5 3x = x + 8 4x = 2x – 20 - x - x - 2x - 2x www.mathsrevision.com 2x = 8 2x = -20 (÷ 2) (÷ 2) x = 4 x = -10 Created by Mr. Lafferty Maths Dept.

  17. Equations & Inequalities Harder Equations Examples MTH 3-15a MTH 4-15a x + 4 = 3x - 10 4x - 1 = 7x + 11 - 4 - 4 + 1 + 1 Swap Round ! Swap Round ! x = 3x - 14 4x = 7x + 12 3x - 14 = x 7x + 12 = 4x + 14 + 14 - 12 - 12 3x = x + 14 7x = 4x - 12 www.mathsrevision.com - x - x - 4x - 4x 2x = 14 3x = -12 (÷ 2) (÷ 3) x = 7 x = -4 Created by Mr. Lafferty Maths Dept.

  18. Equations & Inequalities Harder Equations MTH 3-15a MTH 4-15a Now try Exercise 2 Ch43 (page 173) www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

  19. Starter Questions www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

  20. Equations with Brackets Equations & Inequalities Learning Intention Success Criteria 1. Remember rule for Multiply out brackets. • 1. We are learning how to solve equations with brackets . 2. Apply ‘Balancing Method’ to solve equations. www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

  21. Each group has 2 minutes come up with a method for solving this type of equation Equations & Inequalities Equations with Brackets MTH 3-15a MTH 4-15a Multiply out the brackets first and then Balancing Method Example 3(x – 2) = 33 3x - 6 = 33 + 6 + 6 www.mathsrevision.com 3x = 39 (÷ 3) x = 13 Created by Mr. Lafferty Maths Dept.

  22. Equations & Inequalities Equations with Brackets MTH 3-15a MTH 4-15a Example 5(3x + 2) – 2(4x - 3) = 2x + 36 15x + 10 – 8x + 6 = 2x + 36 Tidy up terms ! 7x + 16 = 2x + 36 - 16 - 16 www.mathsrevision.com 7x = 2x + 20 - 2x - 2x 5x = 20 (÷ 5) x = 4 Created by Mr. Lafferty Maths Dept.

  23. Equations & Inequalities Equations with Brackets MTH 3-15a MTH 4-15a Now try Exercise 3 Ch43 (page 174) www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

  24. Starter Questions 5cm www.mathsrevision.com 11cm Created by Mr. Lafferty Maths Dept.

  25. Equations with Fractions Equations & Inequalities Learning Intention Success Criteria 1. Remember to multiply every term to get rid of fractional term. • 1. We are learning how to solve equations that contain fractional terms. 2. Apply ‘Balancing Method’ www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

  26. Each group has 2 minutes come up with a method for solving this type of equation Equations & Inequalities Equations with Fractions MTH 3-15a MTH 4-15a Example x + 3 = 7 Multiply EVERY term to get rid of fractional term. and then apply ‘Balancing Method’ 1 2 (x 2) x + 6 = 14 - 6 - 6 www.mathsrevision.com x = 8 Created by Mr. Lafferty Maths Dept.

  27. Equations & Inequalities Equations with Fractions MTH 3-15a MTH 4-15a 1 Example x - = 4 Multiply EVERY term to get rid of fractional term. and then apply ‘Balancing Method’ 2 3 (x 4) 4 3x - 2 = 16 + 2 + 2 www.mathsrevision.com 3x = 18 (÷ 3) x = 6 Created by Mr. Lafferty Maths Dept.

  28. Equations & Inequalities Equations with Fractions MTH 3-15a MTH 4-15a Now try Exercise 4 Ch43 (page 175) www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

  29. Starter Questions www.mathsrevision.com 7cm 13cm 15cm Created by Mr. Lafferty Maths Dept.

  30. Harder Fractional Equations with Brackets Equations & Inequalities Learning Intention Success Criteria 1. Apply Balancing Method to solve harder equations. • 1. We are learning how to solve HARDER fractional equations using all the rules learned so far. www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

  31. Equations & Inequalities Harder Fractional Equations with Brackets MTH 3-15a MTH 4-15a Example + 5 = 8 Multiply EVERY term to get rid of fractional term. and then apply ‘Balancing Method’ x + 2 4 (x 4) x + 2 + 20 = 32 Tidy Up ! www.mathsrevision.com x + 22 = 32 - 22 - 22 x = 10 Created by Mr. Lafferty Maths Dept.

  32. Equations & Inequalities Harder Fractional Equations with Brackets MTH 3-15a MTH 4-15a Example (2x – 4) + x = 96 (2x – 4) + x = 16 9 2 4 3 22x = 132 3 2 (÷ 22) (x 6) x = 6 www.mathsrevision.com Tidy Up ! 18x - 36 + 4x = 96 22x - 36 = 96 + 36 + 36 Created by Mr. Lafferty Maths Dept.

  33. Equations & Inequalities Harder Fractional Equations with Brackets MTH 3-15a MTH 4-15a Now try Exercise 5 Ch43 (page 176) www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

  34. Starter Questions www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

  35. Solving Inequalities Equations & Inequalities Learning Intention Success Criteria 1. Understand the term inequality. • 1. We are learning how we can solve inequalities using the same rules we use for equations. 2. Solve inequalities using the same method as equations. www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

  36. Equations & Inequalities Solving Inequalities MTH 3-15a MTH 4-15a The Good News Inequalities are similar to equations except we replace the “=“ with one of the following symbols : www.mathsrevision.com Less than Greater than or equal to Less than or equal to Greater than Created by Mr. Lafferty Maths Dept.

  37. Equations & Inequalities Solving Inequalities MTH 3-15a MTH 4-15a Even Better News ! Solving inequalities is almost identical to solving equations : Example 2x – 1 < 7 NEVER put in an equal sign + 1 + 1 www.mathsrevision.com 2x < 8 (÷ 2) x is any value less than 4 x < 4 Created by Mr. Lafferty Maths Dept.

  38. Equations & Inequalities Solving Inequalities MTH 3-15a MTH 4-15a Example 2(2x – 3) ≥ x + 9 NEVER put in an equal sign 4x – 6 ≥ x + 9 + 6 + 6 4x ≥ x + 15 - x - x www.mathsrevision.com 3x ≥ 15 x is any value greater than or equal to 5 (÷ 3) x ≥ 5 Created by Mr. Lafferty Maths Dept.

  39. Equations & Inequalities Solving Inequalities MTH 3-15a MTH 4-15a The only one to watch out for is when you are dividing by a negative Example 8 – 3m < 2 - 8 - 8 www.mathsrevision.com -3m < -6 FLIP sign (÷ -3) m > 2

  40. Equations & Inequalities Solving Inequalities MTH 3-15a MTH 4-15a Example 5(x – 1) - 8x ≥ -17 Tidy Up ! 5x – 5 - 8x ≥ -17 -3x - 5 ≥ -17 + 5 + 5 FLIP sign www.mathsrevision.com -3x ≥ -12 (÷ -3) x is any value less than or equal to 4 x ≤ 4 Created by Mr. Lafferty Maths Dept.

  41. Equations & Inequalities Solving Inequalities MTH 3-15a MTH 4-15a Now try Exercise 6 Ch43 (page 177) www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

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