Equations

Apr 22, 2023Apr 22, 2023 Created by Mr.Lafferty Maths DeptCreated by Mr.Lafferty Maths Dept

EquationsEquations

Solving EquationsSolving Bracket EquationsSolving both sides Equations

www.

mat

hsre

visio

n.co

m

Solving Inequalities


Starter QuestionsStarter Questionsww

w.m

aths

revi

sion.

com 266 % of £ 2703Q1. Calculate

Q2. Convert 60% to fraction and simplify.

Q3. Convert

Q4. Calculate

45 to a percentage.

3 25 3

Apr 22, 2023Apr 22, 2023 Created by Mr.Lafferty Maths DeptCreated by Mr.Lafferty Maths Deptwww.

mat

hsre

visio

n.co

m Learning IntentionLearning Intention Success CriteriaSuccess Criteria

2.2. Solving harder algebraic Solving harder algebraic equations by using rule equations by using rule repeatedly.repeatedly.

1. To solve harder equations using the rule ‘‘change side change change side change sign’.sign’.repeatedly.repeatedly.

1.1. Know ruleKnow rule‘‘change side change side

change sign’.change sign’.

EquationsEquations


The rule “change side change sign”

www.

mat

hsre

visio

n.co

m The rule we use to solve equations is

EquationsEquations

Write down the opposite of the following :

+opposite isx -

÷opposite isopposite isopposite is

- +÷ x



www.

mat

hsre

visio

n.co

m

2 1 11x

2 10x 2 11 1 10x

Examples

EquationsEquations

+1 opposite

is -1

Check to see if correct !

times by 2

opposite is divide

by 210 52

x


mat

hsre

visio

n.co

mEquationsEquations

The sticks are the same length. Write an equation and solve for x.

3x - 3

18 cm

3 3 18x

3 21x 3 18 3 21x

Check to see if correct !21 73

x


mat

hsre

visio

n.co

m Write down the equation from the number machineand solve it.

25a MultiplyBy 4 Add 1

EquationsEquations

4a + 1 = 254a = 25 – 1 = 244a = 24 a =

24 64


Now try Exercise 1A

Ch4 (page 47)

www.

mat

hsre

visio

n.co

mEquationsEquations



w.m

aths

revi

sion.

com 45% of £ 400Q1. Calculate

Q2. Convert 80% to fraction and simplify.

Q3. Calculate

Q4. Calculate 3 22 35 7

6 3( ) ( )


mat

hsre

visio

n.co


2.2. Solving harder algebraic Solving harder algebraic equations by using rule.equations by using rule.

1. To solve bracket equations using the rule multiply out the brackets multiply out the brackets

then then ‘‘change side change change side change sign’.sign’.

1.1. Know ruleKnow rulemultiply out brackets thenmultiply out brackets then

‘‘change side change side change sign’.change sign’.

Bracket EquationsBracket Equations


mat

hsre

visio

n.co

mBracket EquationsBracket Equations

Example Solve the equation : 2 ( x + 4 ) = 14Solutio

n2( x + 4 ) = 14 Multiply out the bracket first.2x + 8 = 14 Change side change sign

and tidy up2x = 6 Divide both sides by

2 .x = 3 Check if correct !


mat

hsre

visio

n.co


Example Solve the equation : 2 ( 3x + 2 ) = 28Solutio

n2( 3x + 2 ) = 28 Multiply out the bracket first.6x + 4 = 28 Change side change sign

and tidy up6x = 24

Divide both sides by 2 .x = 4 Check if correct !


mat

hsre

visio

n.co


Solve the following equations:

(a) 2 ( x + 4 ) = 14

(b) 3 ( 2x + 5 ) = 27

(c) 5 ( 2x + 6 ) = 100

(d) 4 ( 3x – 5 ) = 40

(e) 7 ( 2 x – 6 ) = 28

(f) 3 ( 4 + 2x ) = 30

x = 3

x = 2

x = 7

x = 5

x = 5

x = 3


Now try Exercise 1B

Ch4 (page 48)

www.

mat

hsre

visio

n.co




w.m

aths

revi

sion.

com 65% of £ 500Q1. Calculate

Q2. Calculate (-2) + (-7) x (-6)

Q3. Calculate

Q4. Calculate 3 17 44 3

2+3×6


mat

hsre

visio

n.co


2.2. Solving harder algebraic Solving harder algebraic equations by using rule.equations by using rule.

1. To solve equations with letters on each side by

getting letters on one getting letters on one side using rule side using rule

‘‘change side change change side change sign’.sign’.

1.1. Know rule letters to one Know rule letters to one sideside

using using ‘‘change side change side


Both Sides Both Sides EquationsEquations


mat

hsre

visio

n.co

mBoth Sides Both Sides EquationsEquations

4m - 3m = 12 - 8

(1) letters to one side

m = 4

(2) Solve as normal

Check correct answer !

4m+8 =3m+12


mat

hsre

visio

n.co


5( m + 4 )

= 3 ( m + 2 )

(1) Multiply out brackets.

5m + 20 = 3m + 6


5m – 3m

= 6 - 20

2m

= -14

m = -7

(3) Solve as normal



mat

hsre

visio

n.co

m The sticks are the same length. Write an equation and solve for x. 3m

+ 6

4m + 1


4m - 3m = 6 - 1


m = 5

(2) Solve as normal


4m+ 1=3m+ 6


mat

hsre

visio

n.co

m

Solve the following equations:

(b) 12 ( x - 4 ) = 4x

(a) 3x + 5 = 2x + 1

(c) 5 ( 2x - 6 ) = 5 (x+1)

x = -4

x = 6

x = 7



Now try Ex2A and 2B

Ch4 (page 48)

www.

mat

hsre

visio

n.co




w.m

aths

revi

sion.

com

Level E

2y+3x+4x+10Q1. Tidy up the expression

Q2. Calculate

Q3. Round to 1 decimal place.

Q4. 12.5 % as a fraction

133 % of 843

(a) 2.34 (b) 10.25(c) 3.23


mat

hsre

visio

n.co


2.2. Solving simple Solving simple inequalities equations.inequalities equations.

1. To solve simple inequalities using the same rules as for equations ‘‘change side change change side change sign’.sign’.

1.1. Know ruleKnow rule‘‘change side change side


InequalitiesInequalities


mat

hsre

visio

n.co

m

The equations you were solving where called equations because they contained an “=“ sign.


greater thanless than

greater than or equal toless than or equal to

There are 4 other symbols Mathematical symbolsThey are called inequalities :


mat

hsre

visio

n.co

mInequalitiesInequalities

Examples : Write in words what each mean.

5 >3-7 > -6

y ≤ -5

x ≥ 2

means 5 is greater than 3means -7 is less than -6means x can take the value2 or greatermeans y can take the value-5 or less

Notice that the arrows

ALWAYS points to the smallest

number


mat

hsre

visio

n.co

m Examples : Write out an inequality for the numbers


(a) 14 and 6(b) -2 and 1(c) -3 and -7(d) 34 and -35

14 > 6-2 < 1-3 > -7

34 > -35


mat

hsre

visio

n.co

m Examples : Choosing from -3, -2, -1, 0 , 1, 2, 3


(a) y < 0(b) y > 2(c) y ≤ -2(d) y > 3

-3, -2, -13-3, -2

No solution


mat

hsre

visio

n.co


The Good NewsSame rule as solving equations




www.

mat

hsre

visio

n.co

m

9 16x

25x 16 9x 18

3x

3 18x

6x

Examples


-9 opposite

is +9

times 3 opposite is divide

by 3




www.

mat

hsre

visio

n.co

m

7 35y

5y

357

y 9 40 4 36m 9 4 40m

36 49

m

Examples



Level E


Now try Ex 3A and 3BCh4 (page 53)

www.

mat

hsre

visio

n.co


Equations

Documents

change sign

lafferty maths deptwww

lafferty maths deptnow

x 6q3

14solution2 x

sideusing change

rule letters

harder equations