# Equations & Inequalities

## Presentation on theme: "Equations & Inequalities"— Presentation transcript:

Equations & Inequalities
Revision of Level 2 Algebra Harder Equations Equations with Brackets Equations with Fractions Harder Fractions Solving Inequalities 1-Apr-17 Created by Mr. Lafferty Maths Dept.

Created by Mr. Lafferty Maths Dept.
Starter Questions 1-Apr-17 Created by Mr. Lafferty Maths Dept.

Equations & Inequalities
Revision of Level 2 Learning Intention Success Criteria To revise Level 2 using the rule ‘Balancing Method’ 1. Understand the process of the ‘Balancing Method’ 2. Solving simple algebraic equations. 1-Apr-17 Created by Mr. Lafferty Maths Dept.

Balancing Method www.mathsrevision.com
1-Apr-17 Created by Mr Lafferty Maths Dept Balancing Method 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 What instrument measures balance How can we go about solving this using balance ?

Created by Mr Lafferty Maths Dept
1-Apr-17 Created by Mr Lafferty Maths Dept Balancing Method Take a small bag away from each side. 4 4 4 4 Take a big bag away from each side. We can see that a big bag is equal to 4 + 4 = 8 kg

Balancing Method Lets solve it using maths. Let P be the weigh
1-Apr-17 Created by Mr Lafferty Maths Dept What symbol should we use for the scales ? Balancing Method Lets solve it using maths. 4 P P P Let P be the weigh of a big bag. 4 4 4 We know that a small bag = 4 Subtract 4 from each side 2P + 4 = P + 12 -4 -4 Subtract P from each side 2P = P + 8 -P -P P = 8

Balancing Method www.mathsrevision.com Let a be the price
1-Apr-17 Created by Mr Lafferty Maths Dept Balancing Method 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 ? a 2 a 2 Let a be the price of an adult ticket. a 2 We know that a child price = £2

Balancing Method For balance we have 5a + 6 = 3a + 16 5a = 3a + 10
1-Apr-17 Created by Mr Lafferty Maths Dept Balancing Method Subtract 3a from each side Subtract 6 from each side For balance we have 2 a 5a + 6 = 3a + 16 a 2 -6 -6 2 2 2 1 5a = 3a + 10 a a -3a -3a Divide each side by 2 2a = 10 a = 5 Adult ticket price is £5

Balancing Method It would be far too time consuming to draw out
1-Apr-17 Created by Mr Lafferty Maths Dept Balancing Method 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
MTH 3-15a MTH 4-15a Revision of Level 2 Reminder ! The Balancing Method Examples x – 5 = 11 x + 8 = 37 + 5 + 5 - 8 - 8 x = 16 x = 29 1-Apr-17 Created by Mr. Lafferty Maths Dept.

Equations & Inequalities
MTH 3-15a MTH 4-15a Revision of Level 2 Reminder ! The Balancing Method Examples 6x = 72 2x = 11 (÷ 6) (÷ 2) x = 12 x = 5.5 1-Apr-17 Created by Mr. Lafferty Maths Dept.

Equations & Inequalities
MTH 3-15a MTH 4-15a Revision of Level 2 Examples 4x – 2 = 34 2x + 9 = 31 + 2 + 2 + 9 + 9 4x = 36 2x = 22 (÷ 4) (÷ 2) x = 9 x = 11 1-Apr-17 Created by Mr. Lafferty Maths Dept.

Equations & Inequalities
MTH 3-15a MTH 4-15a Revision of Level 2 Now try Exercise 1 Ch43 (page 171) 1-Apr-17 Created by Mr. Lafferty Maths Dept.

Created by Mr. Lafferty Maths Dept.
Starter Questions 2x 6x 100o 60o 1-Apr-17 Created by Mr. Lafferty Maths Dept.

Equations & Inequalities
Harder Equations Learning Intention Success Criteria 1. We are learning how to apply balancing method to solve harder equations. Apply balancing method to solve equations with more than one x term. 1-Apr-17 Created by Mr. Lafferty Maths Dept.

Equations & Inequalities
Each group has 2 minutes come up with a method for solving this type of equation Equations & Inequalities MTH 3-15a MTH 4-15a Harder Equations Examples 3x + 2 = x + 10 4x - 5 = 2x - 25 - 2 - 2 + 5 + 5 3x = x + 8 4x = 2x – 20 - x - x - 2x - 2x 2x = 8 2x = -20 (÷ 2) (÷ 2) x = 4 x = -10 1-Apr-17 Created by Mr. Lafferty Maths Dept.

Equations & Inequalities
MTH 3-15a MTH 4-15a Examples Harder Equations x + 4 = 3x - 10 4x - 1 = 7x + 11 - 4 - 4 + 1 + 1 Swap Round ! Swap Round ! x = 3x - 14 4x = 7x + 12 3x - 14 = x 7x + 12 = 4x + 14 + 14 - 12 - 12 3x = x + 14 7x = 4x - 12 - x - x - 4x - 4x 2x = 14 3x = -12 (÷ 2) x = 7 (÷ 3) x = -4 1-Apr-17 Created by Mr. Lafferty Maths Dept.

Equations & Inequalities
Harder Equations MTH 3-15a MTH 4-15a Now try Exercise 2 Ch43 (page 173) 1-Apr-17 Created by Mr. Lafferty Maths Dept.

Created by Mr. Lafferty Maths Dept.
Starter Questions 1-Apr-17 Created by Mr. Lafferty Maths Dept.

Equations & Inequalities
Equations with Brackets Learning Intention Success Criteria 1. Remember rule for Multiply out brackets. 1. We are learning how to solve equations with brackets . 2. Apply ‘Balancing Method’ to solve equations. 1-Apr-17 Created by Mr. Lafferty Maths Dept.

Equations & Inequalities
Each group has 2 minutes come up with a method for solving this type of equation Equations & Inequalities Equations with Brackets MTH 3-15a MTH 4-15a Multiply out the brackets first and then Balancing Method Example 3(x – 2) = 33 3x - 6 = 33 + 6 + 6 3x = 39 (÷ 3) x = 13 1-Apr-17 Created by Mr. Lafferty Maths Dept.

Equations & Inequalities
Equations with Brackets MTH 3-15a MTH 4-15a Example 5(3x + 2) – 2(4x - 3) = 2x + 36 15x + 10 – 8x + 6 = 2x + 36 Tidy up terms ! 7x = 2x + 36 - 16 - 16 7x = 2x + 20 - 2x - 2x 5x = 20 (÷ 5) x = 4 Created by Mr. Lafferty Maths Dept. 1-Apr-17

Equations & Inequalities
Equations with Brackets MTH 3-15a MTH 4-15a Now try Exercise 3 Ch43 (page 174) 1-Apr-17 Created by Mr. Lafferty Maths Dept.

Created by Mr. Lafferty Maths Dept.
Starter Questions 5cm 11cm 1-Apr-17 Created by Mr. Lafferty Maths Dept.

Equations & Inequalities
Equations with Fractions Learning Intention Success Criteria 1. Remember to multiply every term to get rid of fractional term. 1. We are learning how to solve equations that contain fractional terms. 2. Apply ‘Balancing Method’ 1-Apr-17 Created by Mr. Lafferty Maths Dept.

Equations & Inequalities
Each group has 2 minutes come up with a method for solving this type of equation Equations & Inequalities Equations with Fractions MTH 3-15a MTH 4-15a Multiply EVERY term to get rid of fractional term. and then apply ‘Balancing Method’ Example x + 3 = 7 1 2 (x 2) x + 6 = 14 - 6 - 6 x = 8 1-Apr-17 Created by Mr. Lafferty Maths Dept.

Equations & Inequalities
Equations with Fractions MTH 3-15a MTH 4-15a Multiply EVERY term to get rid of fractional term. and then apply ‘Balancing Method’ Example x - = 4 3 4 1 2 (x 4) 3x - 2 = 16 + 2 + 2 3x = 18 (÷ 3) x = 6 1-Apr-17 Created by Mr. Lafferty Maths Dept.

Equations & Inequalities
Equations with Fractions MTH 3-15a MTH 4-15a Now try Exercise 4 Ch43 (page 175) 1-Apr-17 Created by Mr. Lafferty Maths Dept.

Created by Mr. Lafferty Maths Dept.
Starter Questions 7cm 13cm 15cm 1-Apr-17 Created by Mr. Lafferty Maths Dept.

Equations & Inequalities
Harder Fractional Equations with Brackets Learning Intention Success Criteria 1. Apply Balancing Method to solve harder equations. 1. We are learning how to solve HARDER fractional equations using all the rules learned so far. 1-Apr-17 Created by Mr. Lafferty Maths Dept.

Equations & Inequalities
MTH 3-15a MTH 4-15a Harder Fractional Equations with Brackets Multiply EVERY term to get rid of fractional term. and then apply ‘Balancing Method’ Example + 5 = 8 x + 2 4 (x 4) x = 32 Tidy Up ! x + 22 = 32 - 22 - 22 x = 10 1-Apr-17 Created by Mr. Lafferty Maths Dept.

Equations & Inequalities
MTH 3-15a MTH 4-15a Harder Fractional Equations with Brackets Example (2x – 4) x = 16 3 2 22x = 132 (÷ 22) (x 6) x = 6 (2x – 4) + x = 96 9 4 Tidy Up ! 18x - 36 + 4x = 96 22x - 36 = 96 + 36 + 36 1-Apr-17 Created by Mr. Lafferty Maths Dept.

Equations & Inequalities
MTH 3-15a MTH 4-15a Harder Fractional Equations with Brackets Now try Exercise 5 Ch43 (page 176) 1-Apr-17 Created by Mr. Lafferty Maths Dept.

Created by Mr. Lafferty Maths Dept.
Starter Questions 1-Apr-17 Created by Mr. Lafferty Maths Dept.

Equations & Inequalities
Solving Inequalities Learning Intention Success Criteria 1. Understand the term inequality. 1. We are learning how we can solve inequalities using the same rules we use for equations. 2. Solve inequalities using the same method as equations. 1-Apr-17 Created by Mr. Lafferty Maths Dept.

Equations & Inequalities
Solving Inequalities MTH 3-15a MTH 4-15a The Good News Inequalities are similar to equations except we replace the “=“ with one of the following symbols : Less than Greater than or equal to Less than or equal to Greater than 1-Apr-17 Created by Mr. Lafferty Maths Dept.

Equations & Inequalities
MTH 3-15a MTH 4-15a Solving Inequalities Even Better News ! Solving inequalities is almost identical to solving equations : Example 2x – 1 < 7 NEVER put in an equal sign + 1 + 1 2x < 8 (÷ 2) x < 4 x is any value less than 4 1-Apr-17 Created by Mr. Lafferty Maths Dept.

Equations & Inequalities
MTH 3-15a MTH 4-15a Solving Inequalities Example 2(2x – 3) ≥ x + 9 NEVER put in an equal sign 4x – 6 ≥ x + 9 + 6 + 6 4x ≥ x + 15 - x - x 3x ≥ 15 x is any value greater than or equal to 5 (÷ 3) x ≥ 5 1-Apr-17 Created by Mr. Lafferty Maths Dept.

Equations & Inequalities
MTH 3-15a MTH 4-15a Solving Inequalities The only one to watch out for is when you are dividing by a negative Example 8 – 3m < 2 - 8 - 8 -3m < -6 FLIP sign (÷ -3) m > 2 1-Apr-17

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

Equations & Inequalities
MTH 3-15a MTH 4-15a Solving Inequalities Now try Exercise 6 Ch43 (page 177) 1-Apr-17 Created by Mr. Lafferty Maths Dept.