# www mathsrevision com Equations Solving Bracket Equations Solving

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www. mathsrevision. com Equations Solving Bracket Equations Solving both sides Equations Solving Inequalities 12/6/2020 Created by Mr. Lafferty Maths Dept

www. mathsrevision. com Starter Questions Q 1. Calculate Q 2. Convert 60% to fraction and simplify. Q 3. Convert Q 4. Calculate 12/6/2020 to a percentage. Created by Mr. Lafferty Maths Dept

www. mathsrevision. com Equations Learning Intention 1. To solve harder equations using the rule ‘change side change sign’. repeatedly. 12/6/2020 Success Criteria 1. Know rule ‘change side change sign’. 2. Solving harder algebraic equations by using rule repeatedly. Created by Mr. Lafferty Maths Dept

www. mathsrevision. com Equations The rule we use to solve equations is The rule “change side change sign” Write down the opposite of the following : + x opposite is ÷ opposite is 12/6/2020 - opposite is + ÷ opposite is x Created by Mr. Lafferty Maths Dept

www. mathsrevision. com Equations The rule “change side change sign” Examples +1 opposite is -1 times by 2 opposite is divide by 2 Check to see if correct ! 12/6/2020 Created by Mr. Lafferty Maths Dept

- 3 The sticks are the same length. Write an equation and solve for x. 18 cm 3 x www. mathsrevision. com Equations Check to see if correct ! 12/6/2020 Created by Mr. Lafferty Maths Dept

www. mathsrevision. com Equations Write down the equation from the number machine and solve it. 4 a + 1 = 25 4 a = 25 – 1 = 24 4 a = 24 12/6/2020 a= Created by Mr. Lafferty Maths Dept

www. mathsrevision. com Equations Now try Exercise 1 A Ch 4 (page 47) 12/6/2020 Created by Mr. Lafferty Maths Dept

www. mathsrevision. com Starter Questions Q 1. Calculate Q 2. Convert 80% to fraction and simplify. Q 3. Calculate Q 4. Calculate 12/6/2020 Created by Mr. Lafferty Maths Dept

www. mathsrevision. com Bracket Equations Learning Intention 1. To solve bracket equations using the rule 2. multiply out the brackets then ‘change side change sign’. 12/6/2020 Success Criteria 1. Know rule multiply out brackets then ‘change side change sign’. 2. Solving harder algebraic equations by using rule. Created by Mr. Lafferty Maths Dept

Bracket Equations www. mathsrevision. com Example Solve the equation : 2 ( x + 4 ) = 14 Solution 2( x + 4 ) = 14 Multiply out the bracket first. 2 x + 8 = 14 Change side change sign and tidy up 2 x = 6 Divide both sides by 2. x=3 Check if correct ! 12/6/2020 Created by Mr. Lafferty Maths Dept

Bracket Equations www. mathsrevision. com Example Solve the equation : 2 ( 3 x + 2 ) = 28 Solution 2( 3 x + 2 ) = 28 Multiply out the bracket first. 6 x + 4 = 28 Change side change sign and tidy up 6 x = 24 Divide both sides by 2. x=4 Check if correct ! 12/6/2020 Created by Mr. Lafferty Maths Dept

Bracket Equations Solve the following equations: www. mathsrevision. com (a) 2 ( x + 4 ) = 14 (d) x=3 (b) x=5 3 ( 2 x + 5 ) = 27 (e) x=2 (c) 7 ( 2 x – 6 ) = 28 x=5 5 ( 2 x + 6 ) = 100 (f) 3 ( 4 + 2 x ) = 30 x=3 x=7 12/6/2020 4 ( 3 x – 5 ) = 40 Created by Mr. Lafferty Maths Dept

www. mathsrevision. com Bracket Equations Now try Exercise 1 B Ch 4 (page 48) 12/6/2020 Created by Mr. Lafferty Maths Dept

www. mathsrevision. com Starter Questions Q 1. Calculate Q 2. Calculate (-2) + (-7) x (-6) Q 3. Calculate Q 4. Calculate 12/6/2020 Created by Mr. Lafferty Maths Dept

www. mathsrevision. com Both Sides Equations Learning Intention 1. To solve equations with letters on each side by 2. getting letters on one side using rule ‘change side change sign’. 12/6/2020 Success Criteria 1. Know rule letters to one side 2. using ‘change side change sign’. 2. Solving harder algebraic equations by using rule. Created by Mr. Lafferty Maths Dept

www. mathsrevision. com Both Sides Equations (1) letters to one side 4 m - 3 m = 12/6/2020 12 - 8 4 (2) Solve as normal Check correct answer ! Created by Mr. Lafferty Maths Dept

www. mathsrevision. com Both Sides Equations 5( m + 4 ) = 3 ( m + 2 ) 5 m + 20 = 3 m + 6 5 m – 3 m = 6 - 20 (1) Multiply out brackets. (2) letters to one side (3) Solve as normal 2 m = -14 m = 12/6/2020 -7 Check correct answer ! Created by Mr. Lafferty Maths Dept

6 + 4 m + 1 The sticks are the same length. Write an equation and solve for x. 3 m www. mathsrevision. com Both Sides Equations (1) letters to one side 4 m - 3 m = 12/6/2020 6 -1 5 (2) Solve as normal Check correct answer ! Created by Mr. Lafferty Maths Dept

Both Sides Equations Solve the following equations: www. mathsrevision. com (a) 3 x + 5 = 2 x + 1 x = -4 (b) 12 ( x - 4 ) = 4 x x=6 (c) 5 ( 2 x - 6 ) = 5 (x+1) x=7 12/6/2020 Created by Mr. Lafferty Maths Dept

www. mathsrevision. com Both Sides Equations Now try Ex 2 A and 2 B Ch 4 (page 48) 12/6/2020 Created by Mr. Lafferty Maths Dept

Starter Questions www. mathsrevision. com Level E Q 1. Tidy up the expression Q 2. Calculate Q 3. Round to 1 decimal place. (a) Q 4. 12/6/2020 2. 34 (b) 10. 25 (c) 12. 5 % as a fraction Created by Mr. Lafferty Maths Dept 3. 23

www. mathsrevision. com Inequalities Learning Intention 1. To solve simple inequalities using the same rules as for equations ‘change side change sign’. 12/6/2020 Success Criteria 1. Know rule ‘change side change sign’. 2. Solving simple inequalities equations. Created by Mr. Lafferty Maths Dept

www. mathsrevision. com 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 : greater than or equal to less than or equal to 12/6/2020 Created by Mr. Lafferty Maths Dept

www. mathsrevision. com Inequalities Notice that the Examples : Write in words what each mean. arrows ALWAYS points means 5 istogreater than the smallest 5 >3 number -7 > -6 x≥ 2 y ≤ -5 12/6/2020 3 means -7 is less than -6 means x can take the value 2 or greater means y can take the value -5 or less Created by Mr. Lafferty Maths Dept

www. mathsrevision. com Inequalities Examples : Write out an inequality for the numbers (a) 14 and 6 14 > 6 (b) -2 and 1 -2 < 1 (c) -3 and -7 -3 > -7 (d) 34 and -35 12/6/2020 34 > -35 Created by Mr. Lafferty Maths Dept

www. mathsrevision. com Inequalities Examples : Choosing from -3, -2, -1, 0 , 1, 2, 3 (a) y<0 -3, -2, -1 (b) y>2 3 (c) y ≤ -2 -3, -2 (d) y>3 12/6/2020 No solution Created by Mr. Lafferty Maths Dept

www. mathsrevision. com Inequalities The Good News Same rule as solving equations The rule “change side change sign” 12/6/2020 Created by Mr. Lafferty Maths Dept

www. mathsrevision. com Inequalities The rule “change side change sign” Examples -9 opposite is +9 Check to see if correct ! 12/6/2020 Created by Mr. Lafferty Maths Dept times 3 opposite is divide by 3

Inequalities www. mathsrevision. com Level E The rule “change side change sign” Examples Check to see if correct ! 12/6/2020 Created by Mr. Lafferty Maths Dept

www. mathsrevision. com Inequalities Now try Ex 3 A and 3 B Ch 4 (page 53) 12/6/2020 Created by Mr. Lafferty Maths Dept