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a) Conditional Equation
2x – 5 = 9
The equation is true only when the variable is 7.
b) Equation that is a contradiction
105y - 45z = 25y - 45z
It is trying to say that 105y = 25y which is a contradiction.
c) Identity
4x(2+3) = 20x
Regardless of what the value is, this equation will be true.

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a) 3x + 4 = 2x + 1
The condition is the same factor eg. x.

b)3x +4 = 3x +1
The contradiction is when one of the 3x is moved to the other side of the equation, they would cancel each other out.

c)  3(x+2) = 3x +6
The identity is the bracket expression expanded

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a) conditional
: 9x + 2 =11x
It only makes sense if x = 1
b) contradiction
: 4x + 3 = 4x + 213
4x + 3 cannot be the same as 4x + 213 because one is alot bigger
c) Identity
45(10x + 10) = 450x + 450
x could be anything and it still makes sence.

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a) Conditional equation
2x - x = 9
Conditional equations are only true if the variable is a certain number, like in this equation, this equation is only true if the variable of x is 9.
b) equation that is a contradiction
y = y + 2
equations that are a contradiction means that whatever number the variable is, the equation is still wrong like in this equation.
c) identity
4(a + 1) = 4a + 4
This equation is regardless of what number the variable is, the equation is still true

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(a) Conditional Equation:
x * 5 = 25
The equation is true only when x is 5
(b) Equation that is a contradiction:
5m + 2 = 5m -2
It is not possible to find a value of m when LHS = RHS

(c) Identitiy:
5 (6x+8x) = 30x + 40x
All values of the equation is equal

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(a) Conditional Equation:10x+10=9x+15
(b)Equation that is a contradiction:a+69=a+420
(c)Identity:69(d+420)=69d+28980

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a) Conditional Equation
7z + 5 = 4z + 20
The equation will only be true when z = 5
b)Contradiction Equation
6y + 4 = 6y + 8
Its impossible to find the value. of y
c)Identity Equation
2 (5x + 4) = 10x + 8
The values in the equation are all equal

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Using the illustrations given, make an attempt to understand what it means for each type of equations.

Give an example of each of type of equation and briefly describe the characteristics.

Just TYPE the answers. You do NOT need to take photo.

Organise your answer in the following way:

(a) Conditional Equation:

(b) Equation that is a contradiction:

(c) Identitiy:

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(a) Conditional Equation:
p^2 = 100
The equation is true only when p is either 10 or -10

(b) Equation that is a contradiction:
4m + 1 = 4m -1
It is nto possibel to find a value of m when LHS = RHS

(c) Identitiy:
(A + B)(A - B) = A^2 - B^2
It is true for all values of A and B

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(a)Conditional Equation:
3x + 4=3x + 2
the 3x is the same for both sides but not the plus 4 and plus 2.
(b)contradicting equation:
3x + 4=x + 1
none of the variables are the same
(c)Identity:
3(2+x)=3x + 6
All the variables are true.

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(a) Conditional Equation:
2x – 5 = 9 is conditional because it is only true for x = 7.

(b) Equation that is a contradiction:
4z -21 = 4z +21
It is not possible to find a value of z when LHS = RHS

(c) Identitiy:
3(m+21 m) = 66m
The equation will be true for all values of x

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Conditional Equation:
5x + 4 = 4x + 2
Both (3x +4) and (2x + 1) definitely cannot be equal, if they are all positive numbers. They could be equal if x was a negative number.

Equation that is a contradiction:
10x + 5 = 10x + 3
Both statements are equal. However, only one value of both statements are different.

Identity:
3 (2 + 4) = 18
An equation true for all parts of the variable.
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(a) Conditional Equation:
a+b^2=200-(-81)

(b) Equation that is a contradiction:
a+69=a*69

(c) Identitiy:
100+256=(10+13)(10-13)

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Conditional: Such an equation is only true for some variables or values, so x has only one or more possible answers

Take for instance 2x - 2 = 3x - 1

Equation at is contradictory: the equation is basically not correct

Identity: an identity is always true no matter what x is

For example
A squared - B squared = (A+B)(A-B)

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(a) 6b + 6 = 4b +1
(b) 4a + 2 = 4a +1
(c) 4(x) = 4x

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(a) 3a + 6 = 2a + 8
(b) 3b +1 = 3b -1
(c) 2 (3a +2) = 6a +4

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a) conditional equation
4x + 6 = 10x
the equation is only true when x = 1

b) equations that is a contradiction
8f + 2 = 8f + 8
it is not possible to fins a value of a when LHS=RHS

c) identity
8(10 + 5x) = 80 + 40x
all values of the equation are equal.

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a. Conditional Equation
5x + 8 = 4x +4
the equation is only true when x =-4
b. 5x + 5 = 5x - 10
It is not possible to find the value of x when LHS = RHS
c. 4(2x+1) = 8x + 4
all values in the equation are equal

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(a) Conditional equation
3y+2 = 5y-8
y must be equal to 5
(b) Equation that is a contradiction
2x+1 = 2x+4
this is not true for the value of y
(c) Identity
6(y + 1) = 6y + 1
the values in the equation are all equal

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a) Conditional equation
2x+3= 5x-1
-    This is only true when x=2
b) Contradicting equation  3w+1=3w+2
-    It is not possible to find the value of w when LHS=RHS
c) Identity
5(x+4)=5x+20
- All the variables of the equation are true.

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a)conditional equation
3b+5=4b-5
The equation is only true when b=10.
b)contradicting equation
2c+3=2c+6
It is not true for any value of the variable.
C)Identity
4(d+3)=4d+12
all variables of the equation are true.

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a) 3x + 2 = 5x - 8
x must be equal to 5
b) 4y + 1 = 4y + 2
this is not true for any value of y
c) 3(z + 1) = 3z + 3

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(a) Conditional format
4x - 5 = 69
The equation is only true if x is 16

(b) Equation that is a contradiction
4a - 10 = 3a - 10
It is not possible to find a value of a when LHS = RHS

(c) Identity
4(p + 7) = 4p + 28
All values in the equation are equal

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(a) Conditional Equation:
6x + 7 = 4x + 2
The equation is only true when x = 2.5
(b) Equation that is a contradiction:
3x + 9 = 3x + 8
It is not possible to find the value of x when LHS = RHS.
(c) Identity:
3 ( x + 8 )= 3x +24
All variables of the equation are true.

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a) 3x + 2 = 5x - 8
x = 5
b) 4y + 1 = 4y + 2
this is not true for any value of y
c) 3(z + 1) = 3z + 3

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(a) Conditional Equation:
3x + 7 = 7x + 3
The equation is only true when x = 1

(b) Equation that is a contradiction:
2y - 3 = 2y + 3
It is not possible to find the value of y when LHS = RHS

(c) Identitiy:
5z(4-9) = -25z
The equation will be true for all values of z

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a) conditional equation
4y+7=2y+5
the equation is only true when y=-1

b) equations that is a contradiction
7a+1=7a+7
it is not possible to fins a value of a when LHS=RHS

c) identity
4(x+4)=4x+4^2
all values of the equation are equal.

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(a) Conditional Equation
2x = 4
This is only true when x = 2
(b) Contradictory Equation
x = -x
This equation is invalid as a negative term is not equal to a positive term even if their absolute value is the same
(c) Identity
5(x + 5x) = 30x
This is true regardless of the value of x

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(a) Conditional Equation:
69x - 420 = 0
The equation is true only when x is 140/23

(b) Equation that is a contradiction:
x(x - 2) = x^2 - 2x
It is not possible to find a value of    when LHS = RHS

(c) Identity:
(D + P) ^2 = D^2 + 2DP + P^2
It is true for all values of D and P