Equations Inequalities www mathsrevision com MTH 3 15

Equations & Inequalities www. mathsrevision. com MTH 3 -15 a MTH 4 -15 a Revision of Basics Harder Equations with Brackets Equations with Fractions Solving Inequalities 21 -May-21 Created by Mr. Lafferty Maths Dept.

Starter Questions www. mathsrevision. com MTH 3 -15 a MTH 4 -15 a 21 -May-21 Created by Mr. Lafferty Maths Dept.

Equations & Inequalities Revision of Basics www. mathsrevision. com MTH 3 -15 a MTH 4 -15 a Learning Intention Success Criteria 1. To revise Level 2/3 using the rule ‘Balancing Method’ 1. Understand the process of the ‘Balancing Method’ 2. Solving simple algebraic equations. 21 -May-21 Created by Mr. Lafferty Maths Dept.

21 -May-21 Created by Mr Lafferty Maths Dept Balancing Method www. mathsrevision. com MTH 3 -15 a MTH 4 -15 a Kirsty goes to the shops every week to buy some potatoes. She always buys the same total weight. One week she buys 2 large bags and 1 small bag. The following week she buys 1 large bag and 3 small bags. If a small bags weighs 4 kgs. How much does a large bag weigh? 4 4 4 How can we go about What instrument solving this using measures balance ? 4

21 -May-21 Created by Mr Lafferty Maths Dept Balancing Method www. mathsrevision. com MTH 3 -15 a MTH 4 -15 a Take a small bag away from each side. Take a big bag away from each side. We can see that a big bag is equal to 4 + 4 = 8 kg 4 4

21 -May-21 Created by Mr Lafferty Maths Dept Balancing Method What symbol should we use for the scales ? MTH 3 -15 a MTH 4 -15 a www. mathsrevision. com Lets solve it using maths. Let P be the weigh of a big bag. P P 4 We know that a small bag = 4 2 P + 4 = P + 12 -4 -4 2 P = P + 8 -P -P P=8 Subtract 4 from each side Subtract P from each side P 4 4 4

21 -May-21 Created by Mr Lafferty Maths Dept Balancing Method www. mathsrevision. com MTH 3 -15 a MTH 4 -15 a Group of 5 adults and 3 children go to the local swimming. Another group of 3 adults and 8 children also go swimming. The total cost for each group is the same. A child’s ticket costs £ 2. 2 a If a child’s ticket costs £ 2. How much for an adult ticket ? Let a be the price of an adult ticket. 2 a a a 2 We know that a child price = £ 2 2 2 a a 2 2 2

21 -May-21 Created by Mr Lafferty Maths Dept Balancing Method MTH 3 -15 a MTH 4 -15 a www. mathsrevision. com For balance we Subtract 3 a 6 from each side have 2 5 a + 6 = 3 a + 16 a a a 2 5 a = 3 a + 10 a a 2 -6 -3 a 2 a = 10 a= 5 Divide each side by 2 Adult ticket price is £ 5 2 2 2 a a a 2 2 2 1

21 -May-21 Created by Mr Lafferty Maths Dept Balancing Method www. mathsrevision. com MTH 3 -15 a MTH 4 -15 a It would be far too time consuming to draw out the balancing scales each time. We will now review how to use the rules for solving equations.

Equations & Inequalities Revision of Basics www. mathsrevision. com Level 3 Examples 21 -May-21 x + 14 = 22 - 14 32 + y = 101 - 32 y = 69 x =8 Created by Mr. Lafferty Maths Dept.

Equations & Inequalities Revision of Basics www. mathsrevision. com Level 3 Examples Swap ! 72 = g + 40 50 = 35 + m = 50 - 35 21 -May-21 g + 40 = 72 - 35 - 40 m = 15 - 40 g = 32 Created by Mr. Lafferty Maths Dept.

Equations & Inequalities Revision of Basics www. mathsrevision. com Level 3 Examples 21 -May-21 Swap ! 14 = c - 8 - 13 c - 8 = 14 +8 -13 + t = 4 + 13 t = 17 +8 c = 22 Created by Mr. Lafferty Maths Dept.

Equations & Inequalities Revision of Basics www. mathsrevision. com MTH 3 -15 a MTH 4 -15 a Reminder ! The Balancing Method Examples 6 x = 72 6 6 2 x = 11 2 2 x = 5. 5 x = 12 21 -May-21 Created by Mr. Lafferty Maths Dept.

Equations & Inequalities Revision of Basics MTH 3 -15 a MTH 4 -15 a www. mathsrevision. com Examples 4 x – 2 = 34 2 x + 9 = 31 4 x = 36 4 4 2 x = 22 x =9 x = 11 +2 21 -May-21 +2 -9 2 Created by Mr. Lafferty Maths Dept. -9 2

Revision of Basics www. mathsrevision. com MTH 3 -15 a MTH 4 -15 a Now try TJ 3 b Ex 1 Ch 5 (page 48) Are you on Target ? I can ? 21 -May-21 Created by Mr. Lafferty Maths Dept.

Starter Questions www. mathsrevision. com MTH 3 -15 a MTH 4 -15 a 2 x 6 x 100 60 21 -May-21 Created by Mr. Lafferty Maths Dept. o o

Equations & Inequalities Harder Equations www. mathsrevision. com MTH 3 -15 a MTH 4 -15 a Learning Intention Success Criteria 1. We are learning how to apply balancing method to solve harder equations. 21 -May-21 1. Apply balancing method to solve equations with more than one x term. Created by Mr. Lafferty Maths Dept.

Each group has 2 minutes come up with a method for solving this type of. Harder equation. Equations & Inequalities MTH 3 -15 a MTH 4 -15 a www. mathsrevision. com Examples 3 x + 2 = x + 10 -2 -2 3 x = x + 8 -x -x 2 x = 8 2 2 21 -May-21 x =4 4 x - 5 = 2 x - 25 +5 +5 4 x = 2 x – 20 - 2 x 2 x = -20 2 2 Created by Mr. Lafferty Maths Dept. x = -10

Equations & Inequalities Swap. Examples Round ! Swap Harder Equations MTH 3 -15 a MTH 4 -15 a www. mathsrevision. com x + 4 = 3 x - 10 Round ! 3 x - 10 = x + 4 4 x - 1 = 7 x + 11 = 4 x - 1 3 x = x + 14 7 x = 4 x - 12 + 10 -x - 4 x - 11 - 4 x 3 x = -12 3 3 x = -4 2 x = 14 2 2 x =7 21 -May-21 - 11 Created by Mr. Lafferty Maths Dept.

Equations & Inequalities Harder Equations www. mathsrevision. com MTH 3 -15 a MTH 4 -15 a Now try TJ 3 b Ex 2 Ch 5 (page 50) Are you on Target ? I can ? 21 -May-21 Created by Mr. Lafferty Maths Dept.

Starter Questions www. mathsrevision. com MTH 3 -15 a MTH 4 -15 a 21 -May-21 Created by Mr. Lafferty Maths Dept.

Equations & Inequalities Equations with Brackets www. mathsrevision. com MTH 3 -15 a MTH 4 -15 a Learning Intention Success Criteria 1. We are learning how to solve equations with brackets. 21 -May-21 1. Remember rule for Multiply out brackets. 2. Apply ‘Balancing Method’ to solve equations. Created by Mr. Lafferty Maths Dept.

Equations & Inequalities www. mathsrevision. com MTH 3 -15 a MTH 4 -15 a Each group has 2 minutes come up with a method for Equations solving this type of equation with Brackets Multiply out the brackets Example first and then Balancing Method 3(x – 2) = 33 3 x - 6 = 33 +6 +6 3 x = 39 3 3 x = 13 21 -May-21 Created by Mr. Lafferty Maths Dept.

Equations & Inequalities Revision of Basics MTH 3 -15 a MTH 4 -15 a www. mathsrevision. com Examples 2 x - 8 = 26 3(x + 9) = 63 3 x + 27 = 63 2 x = 34 2 2 3 x = 36 3 3 2(x – 4) = 26 +8 +8 x = 17 21 -May-21 Created by Mr. Lafferty Maths Dept. - 27 x = 12

Each group has 2 minutes to come up with a method for solving this type of Harder Equations equation Equations & Inequalities MTH 3 -15 a MTH 4 -15 a www. mathsrevision. com Examples 3(x + 2) = x + 10 3 x + 6 = x + 10 -x -x 2 x + 6 = 10 -6 21 -May-21 -6 2 x = 4 2 2 x =2 4 x - 8 = 2(x + 5) 4 x - 8 = 2 x + 10 - 2 x 2 x - 8 = 10 +8 Created by Mr. Lafferty Maths Dept. +8 2 x = 18 2 2 x =9

Equations & Inequalities Equations with Brackets MTH 3 -15 a MTH 4 -15 a www. mathsrevision. com Example Tidy up terms ! 5(3 x + 2) – 2(4 x - 3) = 2 x + 36 15 x + 10 – 8 x + 6 = 2 x + 36 7 x + 16 = 2 x + 36 - 16 7 x = 2 x + 20 - 2 x Created by Mr. Lafferty Maths Dept. 21 -May-21 - 2 x 5 x = 20 5 5 x=4

Equations & Inequalities Harder Equations www. mathsrevision. com MTH 3 -15 a MTH 4 -15 a Now try TJ 3 b Ex 3 Ch 5 (page 51) Are you on Target ? I can ? 21 -May-21 Created by Mr. Lafferty Maths Dept.

Equations & Inequalities Equations with Brackets www. mathsrevision. com MTH 3 -15 a MTH 4 -15 a Now try Exercise 3 Ch 43 (page 174) 21 -May-21 Created by Mr. Lafferty Maths Dept.

Starter Questions www. mathsrevision. com MTH 3 -15 a MTH 4 -15 a 5 cm 11 cm 21 -May-21 Created by Mr. Lafferty Maths Dept.

Equations & Inequalities Equations with Fractions www. mathsrevision. com MTH 3 -15 a MTH 4 -15 a Learning Intention Success Criteria 1. We are learning how to solve equations that contain fractional terms. 21 -May-21 1. Remember to multiply every term to get rid of fractional term. 2. Apply ‘Balancing Method’ Created by Mr. Lafferty Maths Dept.

Equations & Inequalities www. mathsrevision. com MTH 3 -15 a MTH 4 -15 a Each group has 2 minutes come up with Equations a method for solving this type of equation with Fractions Multiply EVERY term to get rid of fractional term. and then apply ‘Balancing Method’ Example 1 2 (x 2) x+3=7 x + 6 = 14 -6 -6 x=8 21 -May-21 Created by Mr. Lafferty Maths Dept.

Equations & Inequalities Equations with Fractions www. mathsrevision. com MTH 3 -15 a MTH 4 -15 a Multiply EVERY term to get rid of fractional term. and then apply ‘Balancing Method’ Example (x 4) 3 4 x- 1 2 =4 3 x - 2 = 16 +2 +2 3 x = 18 3 3 x=6 21 -May-21 Created by Mr. Lafferty Maths Dept.

Equations & Inequalities www. mathsrevision. com MTH 3 -15 a MTH 4 -15 a Harder Fractional Equations with Brackets Multiply EVERY term to get rid of fractional term. and then apply ‘Balancing Method’ Example (x 4) Tidy Up ! x+2 +5=8 4 x + 20 = 32 x + 22 = 32 - 22 x = 10 21 -May-21 Created by Mr. Lafferty Maths Dept.

Equations & Inequalities MTH 3 -15 a MTH 4 -15 a Harder Fractional Equations with Brackets www. mathsrevision. com Example (x 6) 2 3 (2 x – 4) + x = 16 2 3 Tidy Up ! 9 (2 x – 4) + 4 x = 96 18 x - 36 + 4 x = 96 22 x - 36 = 96 + 36 21 -May-21 + 36 Created by Mr. Lafferty Maths Dept. 22 x = 132 22 22 x=6

Have you updated your Learning book ? Equations & Inequalities Harder Equations www. mathsrevision. com MTH 3 -15 a MTH 4 -15 a Now try TJ 3 b Ex 4 Ch 5 (page 52) Are you on Target ? I can ? 21 -May-21 Created by Mr. Lafferty Maths Dept.

Starter Questions www. mathsrevision. com MTH 3 -15 a MTH 4 -15 a 21 -May-21 Created by Mr. Lafferty Maths Dept.

Equations & Inequalities Solving Inequalities www. mathsrevision. com MTH 3 -15 a MTH 4 -15 a Learning Intention Success Criteria 1. We are learning how we can solve inequalities using the same rules we use for equations. 21 -May-21 1. Understand the term inequality. 2. Solve inequalities using the same method as equations. Created by Mr. Lafferty Maths Dept.

Equations & Inequalities Solving Inequalities MTH 3 -15 a MTH 4 -15 a www. mathsrevision. com The Good News Inequalities are similar to equations except we replace the “=“ with one of the following symbols : Less than Greater than 21 -May-21 Less than or equal to Created by Mr. Lafferty Maths Dept. Greater than or equal to

Equations & Inequalities Solving Inequalities MTH 3 -15 a MTH 4 -15 a www. mathsrevision. com Even Better News ! Solving inequalities is almost identical to solving equations : Example 2 x – 1 < 7 +1 +1 2 x < 8 2 2 x <4 21 -May-21 Created by Mr. Lafferty Maths Dept. NEVER put in an equal sign x is any value less than 4

Equations & Inequalities Solving Inequalities MTH 3 -15 a MTH 4 -15 a www. mathsrevision. com Example 8+ ½m < 14 (x 2) 16 + m < 28 - 16 m < 12 x is any value less than 12 21 -May-21

Equations & Inequalities Solving Inequalities MTH 3 -15 a MTH 4 -15 a www. mathsrevision. com Example 2(2 x – 3) ≥ x + 9 4 x – 6 ≥ x + 9 +6 +6 4 x ≥ x + 15 -x -x 3 x ≥ 15 3 3 21 -May-21 x≥ 5 x is any value greater than or equal to 5

Equations & Inequalities Solving Inequalities www. mathsrevision. com MTH 3 -15 a MTH 4 -15 a Example 5(x – 1) - 3 x ≥ -17 Tidy Up ! 5 x – 5 - 3 x ≥ -17 2 x - 5 ≥ -17 +5 +5 2 x ≥ -12 2 2 21 -May-21 x ≥ -6 x is any value greater than or equal to -6

Have you updated your Learning Log ? Equations Inequalities MTH 3 -15 a MTH 4 -15 a www. mathsrevision. com & Inequalities Now try TJ 3 b Ex 5 Ch 5 (page 53) Are you on Target ? I can ? 21 -May-21 Created by Mr. Lafferty Maths Dept.