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www.mathsrevision.com Equations & Inequalities Revision of Level E Algebra Harder Equations Equations with Brackets Equations with Fractions Harder Fractions Solving Inequalities 30-Apr-17 Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Starter Questions 1. Mulitply out and simplify 3 x( x 6) x( x 3) 2. The ratio of apples to pears is 3 :1. If there are 24 pieces of fruit in total. How many apples are there. 3. 30-Apr-17 Factorise 20 x 4 Created by Mr. Lafferty Maths Dept. Equations & Inequalities www.mathsrevision.com Revision of Level E Learning Intention 1. To revise Level E using the rule ‘change side change sign’. Success Criteria 1. Know rule ‘change side change sign’. 2. Solving simple algebraic equations. 30-Apr-17 Created by Mr. Lafferty Maths Dept. Equations & Inequalities www.mathsrevision.com Revision of Level E Reminder ! We use the rule “change side change sign” Examples x 5 11 x 11 5 x 16 30-Apr-17 x 8 8 x 88 x0 Created by Mr. Lafferty Maths Dept. Equations & Inequalities www.mathsrevision.com Revision of Level E Reminder ! “Opposite of multiplication is division” Examples 2 x 12 x 12 2 x6 30-Apr-17 3n 17 n 17 3 2 x5 3 Created by Mr. Lafferty Maths Dept. Equations & Inequalities www.mathsrevision.com Revision of Level E Reminder ! We use the rule “change side change sign” Examples 2 x 3 11 2 x 11 3 2 x 14 x 14 2 x7 30-Apr-17 4n 7 17 4n 17 7 4n 24 n 24 4 n6 Created by Mr. Lafferty Maths Dept. Equations & Inequalities www.mathsrevision.com Revision of Level E Now try Exercise 1 Ch43 (page 171) 30-Apr-17 Created by Mr. Lafferty Maths Dept. Starter Questions www.mathsrevision.com 1. Find the perimeter and area of the shape. 2x 6x 2. Expand out the brackets 3. 4 y( x y) Find all the missing angles. 100 o 60 30-Apr-17 Created by Mr. Lafferty Maths Dept. o Equations & Inequalities www.mathsrevision.com Harder Equations Learning Intention 1. To explain how we use the same rules to solve harder equations were we have more than one x term. 30-Apr-17 Success Criteria 1. Use same rules to solve equations with more than one x term. Created by Mr. Lafferty Maths Dept. Equations & Inequalities Harder Equations www.mathsrevision.com Same old Rule ! We use the rule “change side change sign” Examples 6 x 1 2 x 21 6 x 2 x 21 1 4 x 20 x 20 4 x5 30-Apr-17 10 x 9 4 x 30 10 x 4 x 30 9 6 x 21 x 21 6 3 1 x3 3 6 2 Created by Mr. Lafferty Maths Dept. Equations & Inequalities www.mathsrevision.com Harder Equations Now try Exercise 2 Ch43 (page 173) 30-Apr-17 Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Starter Questions 1. I have an infinite amount of line symmetry. What is my shape? 2. Calculate 3 1 of 4 8 3. Remove brackets 4(5k - 8) 30-Apr-17 Created by Mr. Lafferty Maths Dept. Equations & Inequalities www.mathsrevision.com Equations with Brackets Learning Intention 1. To show how to solve equations with brackets . 30-Apr-17 Success Criteria 1. Multiply out brackets. 2. Apply ‘change side change sign’ rule. Created by Mr. Lafferty Maths Dept. Equations & Inequalities www.mathsrevision.com Equations with Brackets Multiply out the brackets first and then Apply ‘change side change sign’ rule Examples 2(2 x 3) x 24 4 x 6 x 24 3 x 18 x 18 3 6 30-Apr-17 Created by Mr. Lafferty Maths Dept. Equations & Inequalities Equations with Brackets www.mathsrevision.com Examples 5(3x 2) 2(4 x 3) 2 x 36 15 x 10 8 x 6 2 x 36 7 x 16 2 x 36 5 x 16 36 5 x 20 x 20 5 4 30-Apr-17 Created by Mr. Lafferty Maths Dept. Equations & Inequalities www.mathsrevision.com Equations with Brackets Now try Exercise 3 Ch43 (page 174) 30-Apr-17 Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Starter Questions 1. 5 of 63 7 2. Calculate 2 1 1 1 2 4 5cm 3. Expand the brackets 7 f (3e 9 f ) 4. Calculate the area of the shape. 30-Apr-17 Created by Mr. Lafferty Maths Dept. 11cm Equations & Inequalities www.mathsrevision.com Equations with Fractions Learning Intention 1. To show how to solve equations that contain fractional terms. 30-Apr-17 Success Criteria 1. Multiply every term to get rid of fractional term. 2. Apply ‘change side change sign’ rule. Created by Mr. Lafferty Maths Dept. Equations & Inequalities www.mathsrevision.com Equations with Fractions multiply EVERY term to get rid of fractional term. and Apply ‘change side change sign’ rule Examples 1 x3 7 2 1 2 x 23 2 7 2 x 6 14 x 14 6 8 30-Apr-17 Created by Mr. Lafferty Maths Dept. Multiply EVERY term by 2 Equations & Inequalities www.mathsrevision.com Equations with Fractions multiply EVERY term to get rid of fractional term. and Apply ‘change side change sign’ rule Examples 3 2 3 2 x 2 12 x 12 12 2 4 3 4 3 7 Multiply 9 x 8 24 x 16 9 1 EVERY 9 term by 30-Apr-17 Created by Mr. Lafferty Maths Dept. 12 Equations & Inequalities www.mathsrevision.com Equations with Fractions Now try Exercise 4 Ch43 (page 175) 30-Apr-17 Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Starter Questions 1. 75% of 160 2. Calculate 2 3. Factorise 1 1 -1 2 6 7 f 14e 7cm 4. Calculate the area of the shape. 13cm 30-Apr-17 Created by Mr. Lafferty Maths Dept. 15cm Equations & Inequalities www.mathsrevision.com Harder Fractional Equations with Brackets Learning Intention 1. To show how to solve HARDER fractional equations using all the rules learned so far. 30-Apr-17 Success Criteria 1. Know all rules learned so far. 2. Use these rules to solve harder equations. Created by Mr. Lafferty Maths Dept. Equations & Inequalities www.mathsrevision.com Harder Fractional Equations with Brackets multiply EVERY term to get rid of fractional term. and Apply ‘change side change sign’ rule Examples ( x 1) x 1 3 4 3 6 4 6 3 3 3 x 1 12 18 x 18 13 5Multiply EVERY 30-Apr-17 Created by Mr. Lafferty Maths Dept. term by 3 Equations & Inequalities Harder Fractional Equations with Brackets www.mathsrevision.com Example 3 2 Multiply (2 x 1) x 1 EVERY term by 4 3 12 3 2 12 (2 x 1) 12 x 12 1 4 3 9(2 x 1) 8 x 12 18 x 9 8 x 12 21 26 x 21 x 26 30-Apr-17 Created by Mr. Lafferty Maths Dept. Equations & Inequalities www.mathsrevision.com Harder Fractional Equations with Brackets Now try Exercise 5 Ch43 (page 176) 30-Apr-17 Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Starter Questions 1. 5.67 + 2.3 - 0.07 2. Find the highest common factor for (a) 8 and 12 (b) 20x and 48x 3. Calculate 6b2 + 5a2b when 30-Apr-17 Created by Mr. Lafferty Maths Dept. a = (-1) b = (-2) Equations & Inequalities www.mathsrevision.com Solving Inequalities Learning Intention 1. To show how we can solve inequalities using the same rules we use for equations. 30-Apr-17 Success Criteria 1. Understand the term inequality. 2. Solve inequalities using the same method as equations. Created by Mr. Lafferty Maths Dept. Equations & Inequalities Solving Inequalities www.mathsrevision.com The Good News Inequalities are similar to equations except we replace the “=“ with one of the following symbols : " < "," > "," "or " " Less than Greater than 30-Apr-17 Less than or equal to Created by Mr. Lafferty Maths Dept. Greater than or equal to Equations & Inequalities Solving Inequalities www.mathsrevision.com Even Better News ! Solving inequalities is almost identical to solving equations : Example 1 2x 1 7 2x 7 1 2x 8 x4 30-Apr-17 x is any value less than 4 Created by Mr. Lafferty Maths Dept. Equations & Inequalities Solving Inequalities www.mathsrevision.com Solving inequalities is almost identical to solving equations : Example 2 2(2 x 3) x 9 4x 6 x 9 3x 6 9 x 15 3 3 x 15 x 5 x is any value greater than or equal to 5 30-Apr-17 Created by Mr. Lafferty Maths Dept. Equations & Inequalities Solving Inequalities www.mathsrevision.com The only one to watch out for is when you are dividing by a negative Example 8 – 3m < 2 -3m < -6 Subtract 8 from each side m > -6 Divide across by -3 and change the Sign -3 So m > 2 30-Apr-17 Equations & Inequalities Solving Inequalities Example 2 5( x – 1 ) - 8x ≥ - 17 5x – 5 – 8x ≥ - 17 - 3x - 5 ≥ - 17 - 3x ≥ - 12 x 30-Apr-17 ≤ -12 -3 So x ≤ 4 Equations & Inequalities www.mathsrevision.com Solving Inequalities Now try Exercise 6 Ch43 (page 177) 30-Apr-17 Created by Mr. Lafferty Maths Dept.