Equations & Inequalities

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## Equations & Inequalities

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**Equations & Inequalities**Revision of Level E Algebra Harder Equations Equations with Brackets www.mathsrevision.com Equations with Fractions Harder Fractions Solving Inequalities Created by Mr. Lafferty Maths Dept.**Starter Questions**www.mathsrevision.com Created by Mr. Lafferty Maths Dept.**Revision of Level E**Equations & Inequalities Learning Intention Success Criteria • To revise Level E using the rule • ‘change side change sign’. • 1. Know rule • ‘change side change sign’. • 2. Solving simple algebraic equations. www.mathsrevision.com Created by Mr. Lafferty Maths Dept.**Equations & Inequalities**Revision of Level E Reminder ! We use the rule “change side change sign” Examples www.mathsrevision.com Created by Mr. Lafferty Maths Dept.**Equations & Inequalities**Revision of Level E Reminder ! “Opposite of multiplication is division” Examples www.mathsrevision.com Created by Mr. Lafferty Maths Dept.**Equations & Inequalities**Revision of Level E Reminder ! We use the rule “change side change sign” Examples www.mathsrevision.com Created by Mr. Lafferty Maths Dept.**Equations & Inequalities**Revision of Level E Now try Exercise 1 Ch43 (page 171) www.mathsrevision.com Created by Mr. Lafferty Maths Dept.**100o**60o Starter Questions 2x 6x www.mathsrevision.com Created by Mr. Lafferty Maths Dept.**Harder Equations**Equations & Inequalities Learning Intention Success Criteria • Use same rules to solve equations with more than one x term. • 1. To explain how we use the same rules to solve harder equations were we have more than one x term. www.mathsrevision.com Created by Mr. Lafferty Maths Dept.**Equations & Inequalities**Harder Equations Same old Rule ! We use the rule “change side change sign” Examples www.mathsrevision.com Created by Mr. Lafferty Maths Dept.**Equations & Inequalities**Harder Equations Now try Exercise 2 Ch43 (page 173) www.mathsrevision.com Created by Mr. Lafferty Maths Dept.**Starter Questions**www.mathsrevision.com Created by Mr. Lafferty Maths Dept.**Equations with Brackets**Equations & Inequalities Learning Intention Success Criteria 1. Multiply out brackets. • 1. To show how to solve equations with brackets . 2. Apply ‘change side change sign’ rule. www.mathsrevision.com Created by Mr. Lafferty Maths Dept.**Equations & Inequalities**Equations with Brackets Multiply out the brackets first and then Apply ‘change side change sign’ rule Examples www.mathsrevision.com Created by Mr. Lafferty Maths Dept.**Equations & Inequalities**Equations with Brackets Examples www.mathsrevision.com Created by Mr. Lafferty Maths Dept.**Equations & Inequalities**Equations with Brackets Now try Exercise 3 Ch43 (page 174) www.mathsrevision.com Created by Mr. Lafferty Maths Dept.**Starter Questions**5cm www.mathsrevision.com 11cm Created by Mr. Lafferty Maths Dept.**Equations with Fractions**Equations & Inequalities Learning Intention Success Criteria 1. Multiply every term to get rid of fractional term. • 1. To show how to solve equations that contain fractional terms. 2. Apply ‘change side change sign’ rule. www.mathsrevision.com Created by Mr. Lafferty Maths Dept.**Equations & Inequalities**Equations with Fractions multiply EVERY term to get rid of fractional term. and Apply ‘change side change sign’ rule Examples www.mathsrevision.com Multiply EVERY term by 2 Created by Mr. Lafferty Maths Dept.**Equations & Inequalities**Equations with Fractions multiply EVERY term to get rid of fractional term. and Apply ‘change side change sign’ rule Examples www.mathsrevision.com Multiply EVERY term by 12 Created by Mr. Lafferty Maths Dept.**Equations & Inequalities**Equations with Fractions Now try Exercise 4 Ch43 (page 175) www.mathsrevision.com Created by Mr. Lafferty Maths Dept.**Starter Questions**www.mathsrevision.com 7cm 13cm 15cm Created by Mr. Lafferty Maths Dept.**Harder Fractional Equations with Brackets**Equations & Inequalities Learning Intention Success Criteria 1. Know all rules learned so far. • 1. To show how to solve HARDER fractional equations using all the rules learned so far. 2. Use these rules to solve harder equations. www.mathsrevision.com Created by Mr. Lafferty Maths Dept.**Equations & Inequalities**Harder Fractional Equations with Brackets multiply EVERY term to get rid of fractional term. and Apply ‘change side change sign’ rule Examples www.mathsrevision.com Multiply EVERY term by 3 Created by Mr. Lafferty Maths Dept.**Equations & Inequalities**Harder Fractional Equations with Brackets Example Multiply EVERY term by 12 www.mathsrevision.com Created by Mr. Lafferty Maths Dept.**Equations & Inequalities**Harder Fractional Equations with Brackets Now try Exercise 5 Ch43 (page 176) www.mathsrevision.com Created by Mr. Lafferty Maths Dept.**Starter Questions**www.mathsrevision.com Created by Mr. Lafferty Maths Dept.**Solving Inequalities**Equations & Inequalities Learning Intention Success Criteria 1. Understand the term inequality. • 1. To show 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.**Equations & Inequalities**Solving Inequalities 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.**Equations & Inequalities**Solving Inequalities Even Better News ! Solving inequalities is almost identical to solving equations : Example 1 www.mathsrevision.com x is any value less than 4 Created by Mr. Lafferty Maths Dept.**Equations & Inequalities**Solving Inequalities Solving inequalities is almost identical to solving equations : Example 2 www.mathsrevision.com x is any value greater than or equal to 5 Created by Mr. Lafferty Maths Dept.**Equations & Inequalities**Solving Inequalities 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 www.mathsrevision.com m -6 -3 > Divide across by -3 and change the Sign So m > 2**Equations & Inequalities**Solving Inequalities Example 2 5( x – 1 ) - 8x ≥ - 17 5x – 5 – 8x ≥ - 17 - 3x - 5 ≥ - 17 - 3x ≥ - 12 x -12 -3 ≤ So x ≤ 4**Equations & Inequalities**Solving Inequalities Now try Exercise 6 Ch43 (page 177) www.mathsrevision.com Created by Mr. Lafferty Maths Dept.