133 Views

Download Presentation
## Equations and Inequations

- - - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - - -

**Equations and Inequations**Reminder of Solving Equations 1 Reminder of Solving Equations 2 Equations with Fractions More Equations with Fractions Inequalities Solving Inequalities Created by Mr. Lafferty@mathsrevision.com**Starter Questions**Q1. Is the following true or false (A) (-3a) x 5a = -15a (B) (-6x) x (-7y) =-42xy Q2. Are the 2 answers the same ? (a) (-3h)2 = (b) -(3d)2 = Q3. Spilt £64 pounds into the ratio 7:9 Q4. Explain why 0.0675 is equal to 6.75x10-2 Created by Mr. Lafferty@mathsrevision.com**Reminder on**Solving Equations Learning Intention Success Criteria • To remind pupils on how to solve various types of equations • Understand the process of solving equations using • “ the balancing method ” Created by Mr. Lafferty@mathsrevision.com**Reminder on**Solving Equations Multiply out the bracket first and then solve. Example 1 25 5(x - 3) = Substitute value into original equation to check answer 5x - 15 = 25 = 40 5x = 25 + 15 x = 40 ÷ 5 = 8 Created by Mr. Lafferty@mathsrevision.com**Reminder on**Solving Equations 18 18 Example 2 3(x + 1) 6(x - 2) = Solve as normal Substitute value into original equation to check answer = 3x + 3 - 12 6x = 3 6x – 3x -12 = 3 3x -12 = 3 + 12 3x = 15 3x = 5 = 15 ÷ (3) x Created by Mr. Lafferty@mathsrevision.com**Equations and brackets**6 6 Example 3 Tidy up RHS 6 – (y + 2) -3(2 + 2y) = Substitute value into original equation to check answer - y - 2 = 6 - 6y -6 Solve as normal = 4 - y -6 – 6y = 4 -6 - 6y + y = 4 -6 – 5y = 10 – 5y = -2 = 10 ÷ (-5) y Created by Mr. Lafferty@mathsrevision.com**Reminder on**Solving Equations Now try Ex 2.1 Ch5 MIA (page 99) Created by Mr. Lafferty@mathsrevision.com**Starter Questions**Q1. Explain why the following are True or False (a) -3y x 5y = -30y (b) -6q x (-4q) = 24q2 Q2. Is the following true -2a( b – a) = -2ab +4a Q3. Write down the two numbers that multiply to give 8 and subtract to give 2. Created by Mr. Lafferty@mathsrevision.com**Reminder on**Solving Equations Learning Intention Success Criteria • To remind pupils on how to solve equations containing square terms. • Understand the process of solving equations with square terms using • “ the balancing method ” Created by Mr. Lafferty@mathsrevision.com**Equations and brackets**Multiply out the bracket first and then solve. 289 289 Example 1 x2 + 82 FOIL (x + 2)2 = Substitute value into original equation to check answer (x + 2)(x + 2) = x2 + 64 x2 + 4x + 4 = x2 + 64 = 64 4x + 4 4x = 60 x = 60 ÷ 4 = 15 Created by Mr. Lafferty@mathsrevision.com**Equations and brackets**Multiply out the bracket first and then solve. 35 35 Example 2 m2 + 10 m(m + 2) = Substitute value into original equation to check answer m2 + 2m = m2 + 10 2m = 10 m = 10 ÷ 2 = 5 Created by Mr. Lafferty@mathsrevision.com**Equations and brackets**Example 5 : The two areas are equal. Find the value of x. A = (x + 7)(x – 2) (x – 2) (x + 2) A = (x + 2)2 (x + 7) 400 400 Foil (x + 2) (x + 2)2 = (x + 7) (x - 2) Substitute value into original equation to check answer = x2 + 5x - 14 x2 + 4x + 4 Solve in the usual way 4x + 4 = 5x - 14 4 = x - 14 x = 18 Created by Mr. Lafferty@mathsrevision.com**Equations & Pythagoras**x + 3 cm 3cm x + 2 cm Example Using Pythagoras find the length of all sides of the triangle. 25 25 5 Multiplication Table (x + 3)2 = (x + 2)2 + 32 = x2 + 4x + 13 x2 + 6x + 9 Balancing Method 6x + 9 = 4x + 13 4 2x = 4 x = 2 Lengths are 3 , 4 and 5 cm Check !**Equations and brackets**Now try Ex 2.2 Ch5 MIA (page 101) Created by Mr. Lafferty@mathsrevision.com**Starter Questions**Q1. Multiply out. (a) 3y(x - y) = (b) 6q2 (2 - 4q) = Q2. Explain your working to show that if we split 24 into the ratio 1:5 the answer is 4:20 Q3. Writing out in full 5.2 x 10-3 to get 0.052 Is the correct? Created by Mr. Lafferty@mathsrevision.com**Equations & Fractions**Fractional Equations with Brackets Learning Intention Success Criteria 1. Apply Balancing Method to solve fractional equations. • 1. To show how to solve fractional equations using all the rules learned so far. Created by Mr. Lafferty Maths Dept.**Equations & Fractions**Process of solving equations with fractions • Remove any fraction by multiplying each term by the denominator value. • 2. Simplify each side of the equation if possible. • 3. Carry out balancing method to solve equation. Created by Mr. Lafferty Maths Dept.**Equations & Fractions**Equations with Fractions Multiply EVERY term by 5 Created by Mr. Lafferty Maths Dept.**Equations & Fractions**Equations with Fractions Multiply EVERY term by 3 Remove brackets Balancing Method**Equations & Fractions**Equations with Fractions Multiply EVERY term by 4 Tidy up Balancing Method**Equations & Fractions**Now try Ex 3.1 Ch5 MIA (page 103) Created by Mr. Lafferty@mathsrevision.com**Starter Questions**Q1. Find the area of the second shape given the first has area 7w - 14 (w - 2) (w – 5) 3 7 Q2. Split 48 into the ratio 1:3 Q3. In standard form 18294000 is 1.8x107 is this correct? Created by Mr. Lafferty@mathsrevision.com**Equations & Fractions**Learning Intention Success Criteria • To remind pupils on how to solve equations containing fraction terms. • Understand the process of solving equations with fraction terms using • “ the balancing method ” Created by Mr. Lafferty@mathsrevision.com**Equations & Fractions**Equations with Fractions Multiply EVERY term by LCM 12 Tidy up Balancing Method Created by Mr. Lafferty Maths Dept.**Equations & Fractions**Equations with Fractions Multiply EVERY term by LCM 6 Tidy up Balancing Method Created by Mr. Lafferty Maths Dept.**Equations & Fractions**Equations with Fractions Balancing Method Created by Mr. Lafferty Maths Dept.**Equations & Fractions**Now try Ex 4.1 Ch5 MIA (page 106) Created by Mr. Lafferty@mathsrevision.com**Starter Questions**Q1. Solve for x (a) x + 3 = 8 (b) 2x – 14 = 50 Q2. Is this statement true (x – 1) – 3(x + 1) = -2x Q3. Created by Mr. Lafferty@mathsrevision.com**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.**Removing a**Single Bracket Now try Ex 5.1 Ch5 MIA (page 108) Created by Mr. Lafferty@mathsrevision.com**Starter Questions**Q1. Does 579300 = 5.793x105 Q2. Explain why the answer to 4(w + 2) = 6(w + 1) is w = 1 Q3. Created by Mr. Lafferty@mathsrevision.com**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**Balancing Method Add 1 to both sides Solving Inequalities Even Better News ! Solving inequalities is almost identical to solving equations : Tidy up www.mathsrevision.com Divide by 2 both sides x is any value less than 4 Created by Mr. Lafferty Maths Dept.**Equations & Inequalities**Multiply out brackets Solving Inequalities Solving inequalities is almost identical to solving equations : Add 6 to both side Subtract x from each side. Divide both sides by 3 www.mathsrevision.com x is any value greater than or equal to 5 Created by Mr. Lafferty Maths Dept.**Inequalities**Solving Inequalities The only one to watch out for is when you are dividing by a negative Example 1 8 – 3m < 2 -3m < -6 Subtract 8 from each side m -6 -3 > Divide across by -3 and change the Sign So m > 2**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**Inequalities**Now try 6.1 & 6.2 Ch5 MIA (page 110) Created by Mr. Lafferty@mathsrevision.com