Created by Mr.Lafferty Maths Dept

Created by Mr.Lafferty Maths Dept
Equations Solving Equations Solving Bracket Equations Solving both sides Equations Solving Inequalities 8-Apr-19 Created by Mr.Lafferty Maths Dept

Starter Questions Q1. Calculate Q2. Convert 60% to fraction and simplify. Q3. Convert to a percentage. Q4. Calculate 8-Apr-19 Created by Mr.Lafferty Maths Dept

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. 8-Apr-19 Created by Mr.Lafferty Maths Dept

Equations The rule we use to solve equations is The rule “change side change sign” Write down the opposite of the following : + + - - opposite is opposite is x x ÷ ÷ opposite is opposite is 8-Apr-19 Created by Mr.Lafferty Maths Dept

Equations The rule “change side change sign” +1 opposite is -1 Examples Check to see if correct ! times by 2 opposite is divide by 2 8-Apr-19 Created by Mr.Lafferty Maths Dept

Equations The sticks are the same length. Write an equation and solve for x. 3x - 3 Check to see if correct ! 18 cm 8-Apr-19 Created by Mr.Lafferty Maths Dept

Equations www.mathsrevision.com
Write down the equation from the number machine and solve it. 4a + 1 = 25 4a = 25 – 1 = 24 a = 4a = 24 8-Apr-19 Created by Mr.Lafferty Maths Dept

Equations Now try Exercise 1A Ch4 (page 47) 8-Apr-19 Created by Mr.Lafferty Maths Dept

Starter Questions Q1. Calculate Q2. Convert 80% to fraction and simplify. Q3. Calculate Q4. Calculate 8-Apr-19 Created by Mr.Lafferty Maths Dept

Bracket Equations www.mathsrevision.com 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. 8-Apr-19 Created by Mr.Lafferty Maths Dept

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 2x = 6 Divide both sides by 2 . x = 3 Check if correct ! 8-Apr-19 Created by Mr.Lafferty Maths Dept

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 6x = 24 Divide both sides by 2 . x = 4 Check if correct ! 8-Apr-19 Created by Mr.Lafferty Maths Dept

Bracket Equations www.mathsrevision.com 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 (c) 5 ( 2x + 6 ) = 100 (f) 3 ( 4 + 2x ) = 30 x = 7 x = 3 8-Apr-19 Created by Mr.Lafferty Maths Dept

Bracket Equations Now try Exercise 1B Ch4 (page 48) 8-Apr-19 Created by Mr.Lafferty Maths Dept

Starter Questions Q1. Calculate Q2. Calculate (-2) + (-7) x (-6) Q3. Calculate Q4. Calculate 8-Apr-19 Created by Mr.Lafferty Maths Dept

Both Sides Equations www.mathsrevision.com 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. 8-Apr-19 Created by Mr.Lafferty Maths Dept

Both Sides Equations (1) letters to one side 4m - 3m = 12 - 8 (2) Solve as normal m = 4 Check correct answer ! 8-Apr-19 Created by Mr.Lafferty Maths Dept

Both Sides Equations www.mathsrevision.com 5( m + 4 ) = 3 ( m + 2 )
(1) Multiply out brackets. 5m + 20 = 3m + 6 (2) letters to one side 5m – 3m = 6 - 20 (3) Solve as normal 2m = -14 m = -7 Check correct answer ! 8-Apr-19 Created by Mr.Lafferty Maths Dept

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 4m - 3m = 6 - 1 (2) Solve as normal m = 5 Check correct answer ! 8-Apr-19 Created by Mr.Lafferty Maths Dept

Both Sides Equations www.mathsrevision.com
Solve the following equations: (a) 3x + 5 = 2x + 1 x = -4 (b) 12 ( x - 4 ) = 4x x = 6 (c) 5 ( 2x - 6 ) = 5 (x+1) x = 7 8-Apr-19 Created by Mr.Lafferty Maths Dept

Both Sides Equations Now try Ex2A and 2B Ch4 (page 48) 8-Apr-19 Created by Mr.Lafferty Maths Dept

Starter Questions Level E Q1. Tidy up the expression Q2. Calculate Q3. Round to 1 decimal place. (a) 2.34 (b) (c) 3.23 Q % as a fraction 8-Apr-19 Created by Mr.Lafferty Maths Dept

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. 8-Apr-19 Created by Mr.Lafferty Maths Dept

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 greater than or equal to less than less than or equal to 8-Apr-19 Created by Mr.Lafferty Maths Dept

x ≥ 2 Inequalities 5 >3 -7 > -6 y ≤ -5 means 5 is greater than 3
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 y ≤ -5 means y can take the value -5 or less 8-Apr-19 Created by Mr.Lafferty Maths Dept

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 34 > -35 8-Apr-19 Created by Mr.Lafferty Maths Dept

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 No solution 8-Apr-19 Created by Mr.Lafferty Maths Dept

Inequalities The Good News Same rule as solving equations The rule “change side change sign” 8-Apr-19 Created by Mr.Lafferty Maths Dept

The rule “change side change sign”
Inequalities The rule “change side change sign” times 3 opposite is divide by 3 -9 opposite is +9 Examples Check to see if correct ! 8-Apr-19 Created by Mr.Lafferty Maths Dept

Inequalities Level E The rule “change side change sign” Examples Check to see if correct ! 8-Apr-19 Created by Mr.Lafferty Maths Dept

Inequalities Now try Ex 3A and 3B Ch4 (page 53) 8-Apr-19 Created by Mr.Lafferty Maths Dept

Created by Mr.Lafferty Maths Dept

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