Equations & Inequalities

MTH 3-15aMTH 4-15a

21 Apr 202321 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.

Revision of Level 2 Algebra

Harder Equations

Equations & Equations & InequalitiesInequalities

ww

w.m

ath

srevis

ion

.com

Equations with Brackets

Equations with Fractions

Solving Inequalities

Harder Fractions

MTH 3-15aMTH 4-15a


Starter QuestionsStarter Questionsw

ww

.math

srevis

ion

.com 3 ( 6) ( 3)

20 4

2. The ratio of apples to pears is 3:1.

I f there are 24 pieces of f ruit in total.

How many apples are there.

x x x x

x

1. Mulitply out and simplify

3. Factorise

MTH 3-15aMTH 4-15a

21 Apr 202321 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww

w.m

ath

srevis

ion

.com Learning IntentionLearning Intention Success CriteriaSuccess Criteria

2.2. Solving simple algebraic Solving simple algebraic equations.equations.

1. To revise Level 2 using the rule

‘‘Balancing Method’Balancing Method’

Revision of Level 2

1.1. Understand the process of Understand the process of thethe

‘‘Balancing Method’Balancing Method’


MTH 3-15aMTH 4-15a

21 Apr 2021 Apr 202323

Created by Mr Lafferty Maths DeptCreated by Mr Lafferty Maths Dept

Balancing MethodBalancing Methodw

ww

.math

srevis

ion

.com

4

44

4

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?

What instrument measures balance

How can we go about solving this using balance ?

MTH 3-15aMTH 4-15a

21 Apr 2021 Apr 202323



ww

.math

srevis

ion

.com

4 44

4Take 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

MTH 3-15aMTH 4-15a

21 Apr 2021 Apr 202323



ww

.math

srevis

ion

.com

P P4 P

44

4Lets solve it using maths.

Let P be the weigh of a big bag.

We know that a small bag = 4

2P + 4 P + 12

What symbol should we use for

the scales ?

= Subtract 4 from each

side-4 -4

2P=P + 8Subtract P from each

side-P -P

P=8

MTH 3-15aMTH 4-15a

21 Apr 2021 Apr 202323



ww

.math

srevis

ion

.com

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.

If a child’s ticket costs £2. How much for an adult ticket ?

a a 2

a 2

a a 2Let a be the price of an adult ticket.

We know that a child price = £2

2 aa

2 a

2 22

2 22

MTH 3-15aMTH 4-15a

21 Apr 2021 Apr 202323



ww

.math

srevis

ion

.com For balance we have

5a + 6 3a + 16=

Subtract 6 from each

side

-6 -6

5a=3a + 10

Subtract 3a from each

side

-3a -3a

2a=10

a a

a

a a

2

2

2

aa

a

2

2

2

2

22

22

Divide each side by 2

a=5

Adult ticket price is £5

1

MTH 3-15aMTH 4-15a

21 Apr 2021 Apr 202323



ww

.math

srevis

ion

.com

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.


The Balancing Method

ww

w.m

ath

srevis

ion

.com

Revision of Level 2

Reminder !

Examples


MTH 3-15aMTH 4-15a

x – 5 = 11+ 5 + 5

x = 16

x + 8 = 37- 8 - 8

x = 29


The Balancing Method

ww

w.m

ath

srevis

ion

.com

Revision of Level 2

Reminder !

Examples


MTH 3-15aMTH 4-15a

6x = 72

x = 12

(÷ 6)

2x = 11

x = 5.5

(÷ 2)


w.m

ath

srevis

ion

.com

Revision of Level 2

Examples


MTH 3-15aMTH 4-15a

4x – 2 = 34+ 2 + 2

4x = 36

x = 9

(÷ 4)

2x + 9 = 31- 9 - 9

2x = 22

x = 11

(÷ 2)


Now try Exercise 1Ch43 (page 171)

ww

w.m

ath

srevis

ion

.com

Revision of Level 2


MTH 3-15aMTH 4-15a

MTH 3-15aMTH 4-15a



ww

.math

srevis

ion

.com

4 ( )2. Expand out the brackets y x y

1. Find the perimeter and area of the shape.

3. Find all the missing angles.

6x

2x

100o

60o

MTH 3-15aMTH 4-15a


w.m

ath

srevis

ion


1.1. Apply balancing method Apply balancing method to solve equations with to solve equations with more than one x term.more than one x term.

1. We are learning how to apply balancing method to solve harder equations.

Harder Equations


Examples


w.m

ath

srevis

ion

.com

Harder Equations


MTH 3-15aMTH 4-15a

3x + 2 = x + 10- 2 - 2

3x = x + 8

2x = 8

(÷ 2)

- x - x

x = 4

4x - 5 = 2x - 25+ 5 + 5

4x = 2x – 20

2x = -20

(÷ 2)

- 2x - 2x

x = -10

Each group has 2 minutes come up with a method for solving this type of

equation


w.m

ath

srevis

ion

.com

Harder Equations


MTH 3-15aMTH 4-15a

x + 4 = 3x - 10- 4 - 4x = 3x - 14

3x = x + 14

(÷ 2)

+ 14 + 14

x = 7

Swap Round

!3x - 14 = x

- x - x2x = 14

4x - 1 = 7x + 11+ 1 + 1

4x = 7x + 12

7x = 4x - 12

(÷ 3)

- 12 - 12

x = -4

Swap Round

!7x + 12 = 4x

- 4x - 4x3x = -12

Examples



ww

w.m

ath

srevis

ion

.com

Harder Equations


MTH 3-15aMTH 4-15a

MTH 3-15aMTH 4-15a



ww

.math

srevis

ion

.com 1. I have an infi nite amount of line symmetry.

What is my shape?

3 12. Calculate of

4 8

3. Remove brackets 4(5k - 8)

MTH 3-15aMTH 4-15a


w.m

ath

srevis

ion


1. We are learning how to solve equations with brackets .

1. Remember rule for Multiply out brackets.

2. Apply ‘Balancing Method’ to solve equations.




w.m

ath

srevis

ion

.com

Multiply out the brackets first and then

Balancing Method



MTH 3-15aMTH 4-15a

3(x – 2) = 33

3x - 6 = 33

3x = 39

+ 6 + 6

x = 13(÷ 3)

Example


equation

21 Apr 202321 Apr 2023

Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.

ww

w.m

ath

srevis

ion

.com

Example



MTH 3-15aMTH 4-15a

5(3x + 2) – 2(4x - 3) = 2x + 36

7x + 16 = 2x + 36- 16 - 167x = 2x + 20- 2x - 2x

5x = 20(÷ 5)

x = 4

15x + 10 – 8x + 6 = 2x + 36Tidy up terms !



ww

w.m

ath

srevis

ion

.com



MTH 3-15aMTH 4-15a

MTH 3-15aMTH 4-15a



ww

.math

srevis

ion

.com

7 (3 9 )

51. of 63

7

1 12. Calculate 2 1

2 4

3. Expand the brackets

4. Calculate the area of the shape.

f e f

5cm

11cm

MTH 3-15aMTH 4-15a


w.m

ath

srevis

ion


1. We are learning how to solve equations that contain fractional terms.

1. Remember to multiply every term to get rid of fractional term.


2. Apply ‘Balancing Method’



w.m

ath

srevis

ion

.com

Multiply EVERY term to get rid of fractional term.

and then apply ‘Balancing Method’



MTH 3-15aMTH 4-15a

x + 3 = 712

(x 2)x + 6 = 14

x = 8

- 6 - 6


equation Example


w.m

ath

srevis

ion

.com



MTH 3-15aMTH 4-15a

x - = 434

(x 4)3x - 2 = 16

3x = 18

+ 2 + 2

12

(÷ 3)

x = 6



Example



ww

w.m

ath

srevis

ion

.com



MTH 3-15aMTH 4-15a

MTH 3-15aMTH 4-15a



ww

.math

srevis

ion

.com

7 14

1. 75% of 160

1 12. Calculate 2 - 1

2 6

3. Factorise

4. Calculate the area of the shape.

f e 7cm

13cm15cm

MTH 3-15aMTH 4-15a


w.m

ath

srevis

ion


1. We are learning how to solve HARDER fractional equations using all the rules learned so far.

1. Apply Balancing Method to solve harder equations.

Harder Fractional Equations with Brackets



w.m

ath

srevis

ion

.com



MTH 3-15aMTH 4-15a

+ 5 = 8x + 24

(x 4)

x + 2 + 20 = 32

x + 22 = 32- 22 - 22

x = 10



Example

Tidy Up !


w.m

ath

srevis

ion

.com



MTH 3-15aMTH 4-15a

(x 6)

18x

22x - 36 = 96

(÷ 22)x = 6

(2x – 4) + x = 1632

23

(2x – 4) + x = 969 4

22x = 132

- 36 + 4x = 96

Example

Tidy Up !

+ 36 + 36



ww

w.m

ath

srevis

ion

.com



MTH 3-15aMTH 4-15a

MTH 3-15aMTH 4-15a



ww

.math

srevis

ion

.com

2 2

1. 5.67 + 2.3 - 0.07

2. Find the highest common f actor f or

(a) 8 and 12 (b) 20x and 48x

3. Calculate 6b + 5a b when a=(-1) b=(-2)

MTH 3-15aMTH 4-15a


w.m

ath

srevis

ion


1. We are learning how we can solve inequalities using the same rules we use for equations.

1. Understand the term inequality.

2. Solve inequalities using the same method as equations.




w.m

ath

srevis

ion

.com

Inequalities are similar to equations except we replace the “=“ with one of the following symbols :


" <"," >"," "or " "

Less than or

equal to

Greater than or

equal toGreater than

Less than

The Good News


MTH 3-15aMTH 4-15a

MTH 3-15aMTH 4-15a


w.m

ath

srevis

ion

.com

Solving inequalities is almost identical to solving equations :


x is any value less than 4

Even Better News !


Example 2x – 1 < 7+ 1 + 1

2x < 8

x < 4(÷ 2)

NEVER put in an equal sign

MTH 3-15aMTH 4-15a


w.m

ath

srevis

ion

.com



Example2(2x – 3) ≥ x + 9

+ 6 + 6

x ≥ 5

NEVER put in an equal sign

4x ≥ x + 9– 6

4x ≥ x + 15- x - x

x is any value greater than or equal to 5

(÷ 3)

3x ≥ 15

21 Apr 202321 Apr 2023ww

w.m

ath

srevis

ion

.com



The only one to watch out for is when you are dividing by a negative

Example

MTH 3-15aMTH 4-15a

8 – 3m < 2- 8 - 8

-3m < -6

m > 2(÷ -3) FLIP sign

MTH 3-15aMTH 4-15a


w.m

ath

srevis

ion

.com



Example5(x – 1) - 8x ≥ -17

+ 5 + 5

x ≤ 4

5x - 8x ≥ -17– 5

-3x - 5 ≥ -17

x is any value less than or equal to 4

(÷ -3)

-3x ≥ -12

Tidy Up !

FLIP sign



ww

w.m

ath

srevis

ion

.com



MTH 3-15aMTH 4-15a

Documents

Equations & Inequalities