Equations Inequalities www mathsrevision com MTH 3 15

Equations & Inequalities www. mathsrevision. com MTH 3 -15 a MTH 4 -15 a Revision of Level 2 Algebra Harder Equations with Brackets Equations with Fractions Harder Fractions Solving Inequalities 22 -Nov-20 Created by Mr. Lafferty Maths Dept.

Starter Questions www. mathsrevision. com MTH 3 -15 a MTH 4 -15 a 22 -Nov-20 Created by Mr. Lafferty Maths Dept.

Equations & Inequalities Revision of Level 2 www. mathsrevision. com MTH 3 -15 a MTH 4 -15 a Learning Intention Success Criteria 1. To revise Level 2 using the rule ‘Balancing Method’ 1. Understand the process of the ‘Balancing Method’ 2. Solving simple algebraic equations. 22 -Nov-20 Created by Mr. Lafferty Maths Dept.

22 -Nov-20 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

22 -Nov-20 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

22 -Nov-20 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

22 -Nov-20 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

22 -Nov-20 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

22 -Nov-20 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 Level 2 www. mathsrevision. com MTH 3 -15 a MTH 4 -15 a Reminder ! The Balancing Method Examples x – 5 = 11 x + 8 = 37 x = 16 x = 29 +5 22 -Nov-20 +5 -8 Created by Mr. Lafferty Maths Dept. -8

Equations & Inequalities Revision of Level 2 www. mathsrevision. com MTH 3 -15 a MTH 4 -15 a Reminder ! The Balancing Method Examples 6 x = 72 2 x = 11 (÷ 6) (÷ 2) x = 12 22 -Nov-20 x = 5. 5 Created by Mr. Lafferty Maths Dept.

Equations & Inequalities Revision of Level 2 MTH 3 -15 a MTH 4 -15 a www. mathsrevision. com Examples 4 x – 2 = 34 2 x + 9 = 31 4 x = 36 2 x = 22 +2 +2 (÷ 4) -9 (÷ 2) x =9 22 -Nov-20 -9 x = 11 Created by Mr. Lafferty Maths Dept.

Equations & Inequalities Revision of Level 2 www. mathsrevision. com MTH 3 -15 a MTH 4 -15 a Now try Exercise 1 Ch 43 (page 171) 22 -Nov-20 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 22 -Nov-20 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. 22 -Nov-20 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 4 x - 5 = 2 x - 25 -2 +5 3 x = x + 8 -x 4 x = 2 x – 20 -x - 2 x 2 x = 8 (÷ 2) 22 -Nov-20 x =4 +5 - 2 x 2 x = -20 (÷ 2) Created by Mr. Lafferty Maths Dept. x = -10

Equations & Inequalities MTH 3 -15 a MTH 4 -15 a Harder Equations Examples www. mathsrevision. com x + 4 = 3 x - 10 Swap Round ! -4 -4 x = 3 x - 14 = x + 14 4 x - 1 = 7 x + 11 Swap Round ! - 12 -x 22 -Nov-20 x =7 - 12 7 x = 4 x - 12 - 4 x 2 x = 14 (÷ 2) +1 4 x = 7 x + 12 = 4 x 3 x = x + 14 -x +1 - 4 x 3 x = -12 (÷ 3) Created by Mr. Lafferty Maths Dept. x = -4

Equations & Inequalities Harder Equations www. mathsrevision. com MTH 3 -15 a MTH 4 -15 a Now try Exercise 2 Ch 43 (page 173) 22 -Nov-20 Created by Mr. Lafferty Maths Dept.

Starter Questions www. mathsrevision. com MTH 3 -15 a MTH 4 -15 a 22 -Nov-20 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. 22 -Nov-20 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) 22 -Nov-20 Created by Mr. Lafferty Maths Dept. x = 13

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 (÷ 5) Created by Mr. Lafferty Maths Dept. 22 -Nov-20 - 2 x 5 x = 20 x=4

Equations & Inequalities Equations with Brackets www. mathsrevision. com MTH 3 -15 a MTH 4 -15 a Now try Exercise 3 Ch 43 (page 174) 22 -Nov-20 Created by Mr. Lafferty Maths Dept.

Starter Questions www. mathsrevision. com MTH 3 -15 a MTH 4 -15 a 5 cm 11 cm 22 -Nov-20 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. 22 -Nov-20 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 22 -Nov-20 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) 22 -Nov-20 Created by Mr. Lafferty Maths Dept. x=6

Equations & Inequalities Equations with Fractions www. mathsrevision. com MTH 3 -15 a MTH 4 -15 a Now try Exercise 4 Ch 43 (page 175) 22 -Nov-20 Created by Mr. Lafferty Maths Dept.

Starter Questions www. mathsrevision. com MTH 3 -15 a MTH 4 -15 a 7 cm 13 cm 22 -Nov-20 Created by Mr. Lafferty Maths Dept. 15 cm

Equations & Inequalities www. mathsrevision. com MTH 3 -15 a MTH 4 -15 a Harder Fractional Equations with Brackets Learning Intention Success Criteria 1. We are learning how to solve HARDER fractional equations using all the rules learned so far. 22 -Nov-20 1. Apply Balancing Method to solve harder equations. 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 22 -Nov-20 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 22 -Nov-20 + 36 Created by Mr. Lafferty Maths Dept. 22 x = 132 (÷ 22) x=6

Equations & Inequalities www. mathsrevision. com MTH 3 -15 a MTH 4 -15 a Harder Fractional Equations with Brackets Now try Exercise 5 Ch 43 (page 176) 22 -Nov-20 Created by Mr. Lafferty Maths Dept.

Starter Questions www. mathsrevision. com MTH 3 -15 a MTH 4 -15 a 22 -Nov-20 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. 22 -Nov-20 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 22 -Nov-20 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 NEVER put in an equal sign +1 2 x < 8 (÷ 2) 22 -Nov-20 x <4 x is any value less than 4 Created by Mr. Lafferty Maths Dept.

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 NEVER put in an equal sign 4 x ≥ x + 15 -x -x 3 x ≥ 15 (÷ 3) 22 -Nov-20 x≥ 5 Created by Mr. Lafferty Maths Dept. x is any value greater than or equal to 5

Equations & Inequalities Solving Inequalities MTH 3 -15 a MTH 4 -15 a www. mathsrevision. com The only one to watch out for is when you are dividing by a negative Example 8 – 3 m < 2 -8 -8 -3 m < -6 (÷ -3) 22 -Nov-20 m >2 FLIP sign

Equations & Inequalities Solving Inequalities www. mathsrevision. com MTH 3 -15 a MTH 4 -15 a Example 5(x – 1) - 8 x ≥ -17 Tidy Up ! 5 x – 5 - 8 x ≥ -17 -3 x - 5 ≥ -17 +5 +5 -3 x ≥ -12 (÷ -3) 22 -Nov-20 x≤ 4 Created by Mr. Lafferty Maths Dept. FLIP sign x is any value less than or equal to 4

Equations & Inequalities Solving Inequalities www. mathsrevision. com MTH 3 -15 a MTH 4 -15 a Now try Exercise 6 Ch 43 (page 177) 22 -Nov-20 Created by Mr. Lafferty Maths Dept.