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Equations

Equations. Solving Equations. Solving Bracket Equations. Solving both sides Equations. www.mathsrevision.com. Solving Inequalities. Starter Questions. Q1. Calculate. Q2. Convert 60% to fraction and simplify. to a percentage. . Q3. Convert . www.mathsrevision.com. Q4. Calculate .

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Equations

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  1. Equations Solving Equations Solving Bracket Equations Solving both sides Equations www.mathsrevision.com Solving Inequalities Created by Mr.Lafferty Maths Dept

  2. Starter Questions Q1. Calculate Q2. Convert 60% to fraction and simplify. to a percentage. Q3. Convert www.mathsrevision.com Q4. Calculate Created by Mr.Lafferty Maths Dept

  3. Equations Learning Intention Success Criteria • To solve harder equations using the rule • ‘change side change sign’. • repeatedly. • 1. Know rule • ‘change side change sign’. • 2. Solving harder algebraic equations by using rule repeatedly. www.mathsrevision.com Created by Mr.Lafferty Maths Dept

  4. Equations The rule we use to solve equations is The rule “change side change sign” Write down the opposite of the following : + + - - www.mathsrevision.com opposite is opposite is x x ÷ ÷ opposite is opposite is Created by Mr.Lafferty Maths Dept

  5. Check to see if correct ! Equations The rule “change side change sign” +1 opposite is -1 Examples times by 2 opposite is divide by 2 www.mathsrevision.com Created by Mr.Lafferty Maths Dept

  6. Check to see if correct ! Equations The sticks are the same length. Write an equation and solve for x. 3x - 3 18 cm www.mathsrevision.com Created by Mr.Lafferty Maths Dept

  7. Equations Write down the equation from the number machine and solve it. www.mathsrevision.com 4a + 1 = 25 4a = 25 – 1 = 24 a = 4a = 24 Created by Mr.Lafferty Maths Dept

  8. Equations Now try Exercise 1A Ch4 (page 47) www.mathsrevision.com Created by Mr.Lafferty Maths Dept

  9. Starter Questions Q1. Calculate Q2. Convert 80% to fraction and simplify. Q3. Calculate www.mathsrevision.com Q4. Calculate Created by Mr.Lafferty Maths Dept

  10. Bracket Equations Learning Intention Success Criteria • To solve bracket equations using the rule • multiply out the brackets then • ‘change side change sign’. • Know rule • multiply out brackets then • ‘change side change sign’. • 2. Solving harder algebraic equations by using rule. www.mathsrevision.com Created by Mr.Lafferty Maths Dept

  11. Bracket Equations Example Solve the equation : 2 ( x + 4 ) = 14 Solution 2( x + 4 ) = 14 Multiply out the bracket first. 2x + 8 = 14 Change side change sign and tidy up www.mathsrevision.com 2x = 6 Divide both sides by 2 . x = 3 Check if correct ! Created by Mr.Lafferty Maths Dept

  12. Bracket Equations Example Solve the equation : 2 ( 3x + 2 ) = 28 Solution 2( 3x + 2 ) = 28 Multiply out the bracket first. 6x + 4 = 28 Change side change sign and tidy up www.mathsrevision.com 6x = 24 Divide both sides by 2 . x = 4 Check if correct ! Created by Mr.Lafferty Maths Dept

  13. Bracket Equations Solve the following equations: (a) 2 ( x + 4 ) = 14 (d) 4 ( 3x – 5 ) = 40 x = 3 x = 5 (b) 3 ( 2x + 5 ) = 27 (e) 7 ( 2 x – 6 ) = 28 x = 2 x = 5 www.mathsrevision.com (c) 5 ( 2x + 6 ) = 100 (f) 3 ( 4 + 2x ) = 30 x = 3 x = 7 Created by Mr.Lafferty Maths Dept

  14. Bracket Equations Now try Exercise 1B Ch4 (page 48) www.mathsrevision.com Created by Mr.Lafferty Maths Dept

  15. Starter Questions Q1. Calculate Q2. Calculate (-2) + (-7) x (-6) Q3. Calculate www.mathsrevision.com Q4. Calculate Created by Mr.Lafferty Maths Dept

  16. Both Sides Equations Learning Intention Success Criteria • To solve equations with letters on each side by • getting letters on one side using rule • ‘change side change sign’. • Know rule letters to one side • using • ‘change side change sign’. • 2. Solving harder algebraic equations by using rule. www.mathsrevision.com Created by Mr.Lafferty Maths Dept

  17. Both Sides Equations (1) letters to one side 4m - 3m = 12 - 8 (2) Solve as normal Check correct answer ! m = 4 www.mathsrevision.com Created by Mr.Lafferty Maths Dept

  18. Both Sides Equations (1) Multiply out brackets. 5( m + 4 ) = 3 ( m + 2 ) 5m + 20 = 3m + 6 (2) letters to one side 5m – 3m = 6 - 20 (3) Solve as normal www.mathsrevision.com 2m = -14 Check correct answer ! m = -7 Created by Mr.Lafferty Maths Dept

  19. Both Sides Equations The sticks are the same length. Write an equation and solve for x. 3m + 6 4m + 1 (1) letters to one side www.mathsrevision.com 4m - 3m = 6 - 1 (2) Solve as normal Check correct answer ! m = 5 Created by Mr.Lafferty Maths Dept

  20. Both Sides Equations Solve the following equations: (a) 3x + 5 = 2x + 1 x = -4 (b) 12 ( x - 4 ) = 4x x = 6 www.mathsrevision.com (c) 5 ( 2x - 6 ) = 5 (x+1) x = 7 Created by Mr.Lafferty Maths Dept

  21. Both Sides Equations Now try Ex2A and 2B Ch4 (page 48) www.mathsrevision.com Created by Mr.Lafferty Maths Dept

  22. Level E Starter Questions Q1. Tidy up the expression Q2. Calculate Q3. Round to 1 decimal place. www.mathsrevision.com (a) 2.34 (b) 10.25 (c) 3.23 Q4. 12.5 % as a fraction Created by Mr.Lafferty Maths Dept

  23. Inequalities Learning Intention Success Criteria • To solve simple inequalities using the same rules as for equations • ‘change side change sign’. • 1. Know rule • ‘change side change sign’. • 2. Solving simple inequalities equations. www.mathsrevision.com Created by Mr.Lafferty Maths Dept

  24. Inequalities The equations you were solving where called equations because they contained an “=“ sign. There are 4 other symbols Mathematical symbols They are called inequalities : www.mathsrevision.com greater than or equal to greater than less than or equal to less than Created by Mr.Lafferty Maths Dept

  25. Inequalities Notice that the arrows ALWAYS points to the smallest number Examples : Write in words what each mean. 5 >3 means 5 is greater than 3 -7 > -6 means -7 is less than -6 means x can take the value 2 or greater x ≥ 2 www.mathsrevision.com y ≤ -5 means y can take the value -5 or less Created by Mr.Lafferty Maths Dept

  26. Inequalities Examples : Write out an inequality for the numbers (a) 14 and 6 14 > 6 (b) -2 and 1 -2 < 1 www.mathsrevision.com (c) -3 and -7 -3 > -7 (d) 34 and -35 34 > -35 Created by Mr.Lafferty Maths Dept

  27. Inequalities Examples : Choosing from -3, -2, -1, 0 , 1, 2, 3 (a) y < 0 -3, -2, -1 (b) y > 2 3 www.mathsrevision.com (c) y ≤ -2 -3, -2 (d) y > 3 No solution Created by Mr.Lafferty Maths Dept

  28. Inequalities The Good News Same rule as solving equations www.mathsrevision.com The rule “change side change sign” Created by Mr.Lafferty Maths Dept

  29. Check to see if correct ! Inequalities The rule “change side change sign” times 3 opposite is divide by 3 -9 opposite is +9 Examples www.mathsrevision.com Created by Mr.Lafferty Maths Dept

  30. Check to see if correct ! Inequalities Level E The rule “change side change sign” Examples www.mathsrevision.com Created by Mr.Lafferty Maths Dept

  31. Inequalities Now try Ex 3A and 3B Ch4 (page 53) www.mathsrevision.com Created by Mr.Lafferty Maths Dept

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