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Equations
and Inequations
S4 Credit
www.mathsrevision.com
Reminder of Solving Equations 1
Reminder of Solving Equations 2
Equations with Fractions
More Equations with Fractions
Inequalities
Solving Inequalities
29-Apr-17
Created by Mr. [email protected]
Starter Questions
www.mathsrevision.com
S4 Credit
Q1.
Is the following true or false
(A)
(-3a) x 5a = -15a
(B) (-6x) x (-7y) =-42xy
Q2. Are the 2 answers the same ?
(a) (-3h)2 =
(b) -(3d)2 =
Q3. Spilt £64 pounds into the ratio 7:9
Q4. Explain why 0.0675 is equal to 6.75x10-2
29-Apr-17
Created by Mr. [email protected]
Reminder on
Solving Equations
www.mathsrevision.com
S4 Credit
Learning Intention
1. To remind pupils on how to
solve various types of
equations
29-Apr-17
Success Criteria
1. Understand the process of
solving equations using
“ the balancing method ”
Created by Mr. [email protected]
Reminder on
Solving Equations
www.mathsrevision.com
S4 Credit
Multiply out the bracket first
and then solve.
Example 1
Substitute value
into original
equation to
check answer
29-Apr-17
5(x - 3) = 25
5x - 15 = 25
5x =25 + 15 = 40
x = 40 ÷ 5 = 8
Created by Mr. [email protected]
Reminder on
Solving Equations
www.mathsrevision.com
S4 Credit
Example 2
Substitute value
into original
equation to
check answer
18
18
= 3(x + 1)
6x - 12 = 3x + 3
6(x - 2)
Solve as
normal
6x – 3x -12 = 3
3x -12 = 3
3x = 3 + 12
3x = 15
x = 15 ÷ (3) = 5
29-Apr-17
Created by Mr. [email protected]
Equations and brackets
S4 Credit
www.mathsrevision.com
Example 3
Substitute value
into original
equation to
check answer
6
6
-3(2 + 2y) = 6 – (y + 2)
-6 - 6y = 6 - y - 2
-6 – 6y = 4 - y
-6 - 6y + y = 4
-6 – 5y = 4
Tidy up
RHS
Solve as
normal
– 5y = 10
y = 10 ÷ (-5) = -2
29-Apr-17
Created by Mr. [email protected]
Reminder on
Solving Equations
S4 Credit
www.mathsrevision.com
Now try Ex 2.1
Ch5 MIA (page 99)
29-Apr-17
Created by Mr. [email protected]
Starter Questions
www.mathsrevision.com
S4 Credit
Q1.
Explain why the following are True or False
(a)
-3y
Q2.
Is the following true
x
5y = -30y (b)
-6q x (-4q) = 24q2
-2a( b – a) = -2ab +4a
Q3. Write down the two numbers that multiply
to give 8 and subtract to give 2.
29-Apr-17
Created by Mr. [email protected]
Reminder on
Solving Equations
www.mathsrevision.com
S4 Credit
Learning Intention
1. To remind pupils on how to
solve equations containing
square terms.
29-Apr-17
Success Criteria
1. Understand the process of
solving equations with square
terms using
“ the balancing method ”
Created by Mr. [email protected]
Equations and brackets
www.mathsrevision.com
S4 Credit
Multiply out the bracket first
289
and then solve. 289
Example 1
(x + 2)2 = x2 + 82
FOIL
Substitute value
(x + 2)(x + 2) = x2 + 64
into original
equation to
x2 + 4x + 4 = x2 + 64
check answer
4x + 4 = 64
4x = 60
x = 60 ÷ 4 = 15
29-Apr-17
Created by Mr. [email protected]
Equations and brackets
www.mathsrevision.com
S4 Credit
Multiply out the bracket first
and then solve.
35
Example 2
Substitute value
into original
equation to
check answer
29-Apr-17
m(m + 2)
m2 + 2m
2m
m
35
= m2 + 10
= m2 + 10
= 10
= 10 ÷ 2 = 5
Created by Mr. [email protected]
Equations and brackets
S4 Credit
www.mathsrevision.com
Example 5 : The two areas are equal. Find the value of x.
(x + 2)
A = (x +
A = (x + 7)(x – 2) (x – 2)
2)2
400
(x + 2)
Substitute value
into original
equation to
check answer
29-Apr-17
(x + 7)
400
(x + 2)2 = (x + 7) (x - 2)
Foil
x2 + 4x + 4 = x2 + 5x - 14
Solve in the
4x + 4 = 5x - 14
usual way
4 = x - 14
x = 18
Created by Mr. [email protected]
Equations & Pythagoras
S4 Credit
Example
www.mathsrevision.com
Using Pythagoras find the length of all sides of the triangle.
Multiplication
Table
25
25
(x + 3)2 = (x + 2)2 + 32
x2 + 6x + 9 = x2 + 4x + 13
Balancing
6x + 9 = 4x + 13
Method
2x = 4
x=2
Check !
5
x + 3 cm
3cm
x + 2 cm
4
Lengths are
3 , 4 and 5 cm
Equations and brackets
S4 Credit
www.mathsrevision.com
Now try Ex 2.2
Ch5 MIA (page 101)
29-Apr-17
Created by Mr. [email protected]
Starter Questions
S4 Credit
www.mathsrevision.com
Q1.
Multiply out.
(a)
3y(x - y) =
(b)
6q2 (2 - 4q) =
Q2. Explain your working to show that if we
split 24 into the ratio 1:5 the answer is 4:20
Q3. Writing out in full 5.2 x 10-3 to get 0.052
Is the correct?
29-Apr-17
Created by Mr. [email protected]
Equations & Fractions
Fractional Equations with Brackets
www.mathsrevision.com
S4 Credit
Learning Intention
Success Criteria
1. To show how to solve
fractional equations using
all the rules learned so far.
29-Apr-17
1. Apply Balancing Method to
solve fractional equations.
Created by Mr. Lafferty Maths Dept.
Equations & Fractions
S4 Credit
www.mathsrevision.com
Process of solving equations with fractions
1. Remove any fraction by multiplying each
term by the denominator value.
2. Simplify each side of the equation if
possible.
3. Carry out balancing method to solve equation.
29-Apr-17
Created by Mr. Lafferty Maths Dept.
Equations & Fractions
Equations with Fractions
www.mathsrevision.com
S4 Credit
Multiply
EVERY term
by 5
29-Apr-17
y 1

5 3
y
1
 5  5
5
3
5
y
3
Created by Mr. Lafferty Maths Dept.
Equations & Fractions
Equations with Fractions
www.mathsrevision.com
S4 Credit
Multiply
EVERY term
by 3
Balancing
Method
7
m  (m  2)
3
 3m  7(m  2)
 3m  7 m  14
 4m  14
7
m
2
Remove
brackets
Equations & Fractions
Equations with Fractions
www.mathsrevision.com
S4 Credit
Multiply
EVERY term
by 4
Balancing
Method
3
x2 x
4
3
 4x  8  4  x
4
 4 x  8  3x
 x 8
Tidy up
Equations & Fractions
S4 Credit
www.mathsrevision.com
Now try Ex 3.1
Ch5 MIA (page 103)
29-Apr-17
Created by Mr. [email protected]
Starter Questions
www.mathsrevision.com
S4 Credit
Q1. Find the area of the second shape given
the first has area 7w - 14
(w - 2)
(w – 5)
7
3
Q2. Split 48 into the ratio 1:3
Q3. In standard form 18294000 is 1.8x107
is this correct?
29-Apr-17
Created by Mr. [email protected]
Equations & Fractions
www.mathsrevision.com
S4 Credit
Learning Intention
1. To remind pupils on how to
solve equations containing
fraction terms.
29-Apr-17
Success Criteria
1. Understand the process of
solving equations with
fraction terms using
“ the balancing method ”
Created by Mr. [email protected]
Equations & Fractions
www.mathsrevision.com
S4 Credit
Multiply
EVERY term
by LCM 12
Equations with Fractions
x x
 3
4 6
x
x
 12   12   12  3
4
6
 3x  2 x  36
Balancing
Method
 x  36
29-Apr-17
Created by Mr. Lafferty Maths Dept.
Tidy up
Equations & Fractions
www.mathsrevision.com
S4 Credit
Multiply
EVERY term
by LCM 6
Equations with Fractions
y 1 y 1

2
2
3
Tidy up
( y  1)
( y  1)
 6
 6
 6 2
2
3
Balancing
 3( y  1)  2( y  1)  12
29-Apr-17
Created by Mr. Lafferty Maths Dept.
Method
Equations & Fractions
Equations with Fractions
www.mathsrevision.com
S4 Credit
 3( y  1)  2( y  1)  12
 3 y  3  2 y  2  12
 y  5  12
 y  17
29-Apr-17
Created by Mr. Lafferty Maths Dept.
Balancing
Method
Equations & Fractions
S4 Credit
www.mathsrevision.com
Now try Ex 4.1
Ch5 MIA (page 106)
29-Apr-17
Created by Mr. [email protected]
Starter Questions
S4 Credit
www.mathsrevision.com
Q1.
Solve for x
(a)
x+3=8
(b)
2x – 14 = 50
Q2. Is this statement true
(x – 1) – 3(x + 1) = -2x
Q3.
29-Apr-17
1 1
3 1
2 3
Created by Mr. [email protected]
Equations & Inequalities
www.mathsrevision.com
Solving Inequalities
Learning Intention
1. To show how we can solve
inequalities using the same
rules we use for equations.
29-Apr-17
Success Criteria
1. Understand the term
inequality.
2. Solve inequalities using
the same method as
equations.
Created by Mr. Lafferty Maths Dept.
Equations & Inequalities
Solving Inequalities
www.mathsrevision.com
The Good News
Inequalities are similar to equations except
we replace the “=“ with one of the following symbols :
" < " " > " "  " or
Less than
Greater than
29-Apr-17
Less than
or
equal to
Created by Mr. Lafferty Maths Dept.
""
Greater than
or
equal to
Removing a
Single Bracket
S4 Credit
www.mathsrevision.com
Now try
Ex 5.1
Ch5 MIA (page 108)
29-Apr-17
Created by Mr. [email protected]
Starter Questions
S4 Credit
www.mathsrevision.com
Q1.
Does 579300 = 5.793x105
Q2. Explain why the answer to
4(w + 2) = 6(w + 1) is w = 1
Q3.
29-Apr-17
1 3
7 
2 4
Created by Mr. [email protected]
Equations & Inequalities
www.mathsrevision.com
Solving Inequalities
Learning Intention
1. To show how we can solve
inequalities using the same
rules we use for equations.
29-Apr-17
Success Criteria
1. Understand the term
inequality.
2. Solve inequalities using
the same method as
equations.
Created by Mr. Lafferty Maths Dept.
Equations & Inequalities
Solving Inequalities
www.mathsrevision.com
The Good News
Inequalities are similar to equations except
we replace the “=“ with one of the following symbols :
" < " " > " "  " or
Less than
Greater than
29-Apr-17
Less than
or
equal to
Created by Mr. Lafferty Maths Dept.
""
Greater than
or
equal to
Equations
&
Inequalities
Balancing Method
www.mathsrevision.com
Add 1 to
both sides
Solving Inequalities
Even Better News !
Solving inequalities is almost identical to solving equations :
2x 1  7
2x  7 1
2x  8
x4
29-Apr-17
Tidy up
Divide by 2
both sides
x is any value less than 4
Created by Mr. Lafferty Maths Dept.
Equations & Inequalities
Multiply out
brackets
Solving Inequalities
www.mathsrevision.com
Solving inequalities is almost identical to solving equations :
Add 6 to
both side
Divide both
sides by 3
2(2 x  3)  x  9
4x  6  x  9
Subtract x
from each side.
4 x  x  15
x  15  3
3 x  15
x  5 x is any value greater than or equal to 5
29-Apr-17
Created by Mr. Lafferty Maths Dept.
Inequalities
Solving Inequalities
www.mathsrevision.com
S4 Credit
The only one to watch out
for is when you are dividing by a negative
Example 1
8 – 3m < 2
-3m < -6
Subtract 8 from each side
m > -6 Divide across by -3 and change the Sign
-3
So m > 2
Inequalities
Solving Inequalities
S4 Credit
www.mathsrevision.com
Example 2
5( x – 1 ) - 8x
≥ - 17
5x – 5 – 8x ≥ - 17
- 3x - 5 ≥ - 17
- 3x ≥ - 12
x
29-Apr-17
≤
-12
-3
So x ≤ 4
Inequalities
www.mathsrevision.com
S4 Credit
Now try 6.1 & 6.2
Ch5 MIA (page 110)
29-Apr-17
Created by Mr. [email protected]