### Expression and Equation

This is a continuation about algebra. We have covered definitions of the various terms used in algebra such as variables, like terms etc. We discussed about fundamental concepts and differences between expressions and equations.

Go through the site Study Guides and Strategies and attempt the following questions.
1. What is the difference between an equation and an expression?
2. What are the characteristics of a linear expression?
3. What does it mean to solve an equation?
4. Can an equation have multiple solutions?
5. Can an equation has no solution?
Solve the following equations for the value/s of x.
1. 8x - 46 = 2
2. 8x + 46 = 2
3. -8x +46 = 2
4. 8x + 46 = 46
5. 8x + 46 = 8x
1. What is the significance of the solutions of the above equations?
2. Can an equation have multiple solutions or no solution? If so, what is the implication.

1. a)8x - 46 = 2
x=6

b)8x + 46 = 2
x=-6

c)-8x +46 = 2
x=-6

d)8x + 46 = 46
x=0

e)8x + 46 = 8x
x= not possible to deduce.

a) If 8x - 46 = 2,
2 + 46 = 48
8x = 48
x = 48 / 8 = 6

b) If 8x + 46 = 2
46 - 2 = 44
-44 + 46 = 2
8x = -44
x = -44 / 8 = -5.5

c) If -8x + 46 = 2
46 - 2 = 44
-44 + 46 = 2
-8x = (-44)
x = (-44) / (-8) = 5.5

d) If 8x + 46 = 46
46 - 46 = 0
8x = 0
x = 0 / 8 = 0

e) If 8x + 46 = 8x
The following question cannot be define

3. This comment has been removed by the author.

1. 8x - 46 = 2
2 + 46 = 48
8x = 48
x = 6

2. 8x + 46 = 2
2 - 46 = (-44)
8x = (-44)
x = (-5.5)

3. -8x +46 = 2
2 - 46 = (-44)
-8x = (-44)
x = 5.5

4. 8x + 46 = 46
46 - 46 = 0
8x = 0
x = 0

5. 8x + 46 = 8x
The question is undefined as 8x + 46 could never be equal to 8x as 8x must be added with a 0 to give the possible outcome thus this question cannot be solved.

5. 1)8x - 46 = 2
8x=48
x=6
2)8x + 46 = 2
8x=-44
x=-5.5
3)-8x +46 = 2
-8x=-44
x=5.5

4)8x + 46 = 46
x=0
8x + 46 = 8x
0x=-46
This Q cannot be defined.

6. 1) 8x - 46 = 2
8x = 48
x = 6

2) 8x + 46 = 2
46-2 = 8x
44 = 8x
5.5 = x

3) -8x +46 = 2
46-2 = 8x
44 = 8x
5.5 = x

4) 8x + 46 = 46
8x = 46 - 46
8x = 0
x = 0/8 which is undefined.

5) 8x + 46 = 8x

This question is not definable as 8x will always be = to 8x. So having 46 added to one side will cause the whole statement to be unbalanced thus making it a mathematical error.

7. Ques 1. 8x - 46 = 2
8x = 2 + 46
8x = 48
x = 6

Ques 2, 8x + 46 = 2
8x = 2 - 46
8x = -44
x = -5.5

Ques 3. -8x +46 = 2
-8x = 2 - 46
-8x = -44
-x = -5.5
x = 5.5

Ques 4. 8x + 46 = 46
8x = 46 - 46
8x = 0
x = 0

Ques 5. 8x + 46 = 8x
8x = 8x - 46
(Which is impossible)

What is the significance of the solutions of the above equations?

- It shows that the value of the variable is dependent on the answer of the equation.

Can an equation have multiple solutions or no solution? If so, what is the implication.

- A equation can only have one solution, eg. 8x - 46 = 2. There is no other value of x except 6. But, an equation with a variable within can have various type of answers as the final product.

8. 1) 8x - 46 = 2
8x=2+46
8x=48
x=6
2)8x + 46 = 2
8x=-46+2
8x=-44
x=-5.5
3)-8x +46 = 2
-8x = 2 - 46
-8x = -44
-x = -5.5
x = 5.5
4)8x + 46 = 46
8x = 46 - 46
8x = 0
x = 0
5)8x+46=8x
8x-8x=-46????
Frankly speaking, I really think this is the way to do it...but it's different from other people's.

9. a)8x - 46 = 2(ans.)
x Will equal to 6

b)8x + 46 = 2 (ans.)
x Will equal to

-6  c)-8x +46 = 2 (ans.)
x Will equal to

-6  d)8x + 46 = 46 (ans.)
x Will equal to 0

e)8x + 46 = 8x (ans.)
X is Impossible to deduce as the before and after have the same values with an added 46.

1. Equation can be answered but expression can only be simplified.
e.g (Equation - 10=x+15) (Expression - 10x-5y)

2. a mathematical statement that performs functions of addition, subtraction, multiplication, and division

These are examples of linear expressions:
x + 4
2x + 4
2x + 4y

These are not linear expressions:
x2 (no exponents on variables)
2xy + 4 (can't multiply two variables)
2x / 4y (can't divide two variables)
Ö x (no square root sign on variables)

Source:http://www.studygs.net/equations.htm

3. No. It will be a definite answer.
e.g 10=x-5 (x=15)

4. Yes, if only the expression is false.
e.g 3>x = 5<y

11. 1. 8x - 46 = 2
46＋2＝48
48／8＝6
x=6

2. 8x + 46 = 2
2-46=-44
-44/8=-11/2=-5.5
x=5.5

3. -8x +46 = 2
2-46=-44
-44/-8=11/2=5.5
x=5.5

4. 8x + 46 = 46
46-46=0
0/8=0
x=0

5. 8x + 46 = 8x

cannot be done because 46 is a constant so it cannot be ignored

12. 1) 8x - 46 = 2
x = 6

2) 8x + 46 = 2
x = -6

3) 8x + 46 = 2
x = -6

4) 8x + 46 = 46
x = 0

5) 8x + 46 = 8x
x = Undefined.

13. This comment has been removed by the author.

14. What is the difference between an equation and an expression?
Equations has an answer and no variable. An Expression is solved by simplifying and may have a variable.

What are the characteristics of a linear expression?
The linear expression must have a variable.

What does it mean to solve an equation?
To simplify the variable.

Can an equation have multiple solutions?
No. It cannot have multiple solutions.

Can an equation has no solution?
No. It must have one solution.

-Jasper

15. Difference between Equation and Expression
- Equation has an equal sign while expression doesn’t
- Equation can be solved but and expression can only be simplified

Characteristics of Linear Equation
- Has no operations other than addition, subtraction and multiplication of a variable by a constant
- Variables may not be multiplied together or appear in a denominator
- A linear equation does not contain variable with exponents other than 1
- The graph of a linear equation is ALWAYS a line

Can an equation have multiple solution
- An equation cannot have multiple solution

Can an equation has no solution
- An equation must have one solution if not it would not be an equation

16. An equation has a equal sign but the expression does not have an equal sign.

A linear equation is an algebraic equation in which each term is either a constant or the product of a constant and (the first power of) a single variable.

The left hand and the right hand of the equation must be simplified and after simplification, the both sides of the equation must be having the same value

No because there is only one solution and answer to the equation in order to meet the exact value.

No. An equation has one solution.

17. 1) 8x - 46 = 2
x = 6

2) 8x + 46 = 2
x = -6

3) 8x + 46 = 2
x = -6

4) 8x + 46 = 46
x = 0

5) 8x + 46 = 8x
x = Cannot be defined

18. 1)
8x - 46 = 2
8x = 48
x = 6

2)
8x + 46 = 2
8x = (-44)
x = -5.5

3)
-8x +46 = 2
-8x =(-44)
x = 5.5

4)
8x + 46 = 46
8x = 0
x = 0

5)
8x + 46 = 8x
x = not possible

19. This comment has been removed by the author.

20. What is the difference between an equation and an expression?
An equation must be solved, while an expression can only be simplified
What are the characteristics of a linear expression?
It must have a variable.
What does it mean to solve an equation?
To find the value of a variable
Can an equation have multiple solutions?
No, an equation cannot have more than one solution
Can an equation has no solution?
No, an equation must have only one solution

21. This comment has been removed by the author.

1. Equation can be answered but expression can only be simplified.
2. A mathematical statement that performs functions of addition, subtraction, multiplication, and division.
3. Simplifying the terms.
4. no an equation cannot have multiple solutions.
5. No, equations must have a solution.
a)8x - 46 = 2
8x=2+46
8x=48
x=6
b)8x + 46 = 2
8x=2-46
8x=44
x=5.5
c)-8x +46 = 2
-8x=2-46
-8x=-44
-x=-5.5
x=5.5
d)8x + 46 = 46
8x=0
x=0
e)8x + 46 = 8x
8x-8x=-46
x=0/undefined

23. 1. What is the difference between an equation and an expression?
~An expression can only be simplified while an equation can be solved.

2. What are the characteristics of a linear expression?
~ Is an equation between 2 variables that gives a straight line.

3. What does it mean to solve an equation?
~ To find the value of something. e.g. x

4. Can an equation have multiple solutions?
~ No. An equation cannot have multiple solutions.

5. Can an equation has no solution?
~No. An equation will have a solution no matter what.

1. What is the difference between an equation and an expression?
An equation has an answer which can be solved while an expression cannot be solved .
2. What are the characteristics of a linear expression?
In a linear expression , there should be a variable .
3. What does it mean to solve an equation?
To solve an equation means simplifying the statement and the variable .
4. Can an equation have multiple solutions?
No . It cannot have multipe solutions .
5. Can an equation has no solution?
An equation should atleast have a single solution in order to be an equation .

1) 8x - 46 = 2
8x = 2 + 46
x = 6

2) 8x + 46 = 2
8x = 2 - 46
= -44
x = -5.5

3) -8x + 46 = 2
-8x = 2 - 46
= -44
x = 5.5

4) 8x + 46 = 46
8x = 46 - 46
= 0
x = 0

5) 8x + 46 = 8x
Ans = Undefined as x does not have any vlue .

25. 1) 8x - 46 = 2
8x = 46 + 2
8x = 48
x = 48 / 8
x = 6

2) 8x + 46 = 2
8x = 2 - 46
8x = -44
x = -44 / 8
x = -5.5

3) -8x + 46 = 2
-8x = 2 - 46
-8x = -44
x = -44 / -8
x = 5.5

4) 8x + 46 = 46
8x = 46 + 46
8x = 92
x = 92 / 8
x = 11.5

5) 8x + 46 = 8x
This solution cannot be defined

What is the difference between an equation and an expression?
An equation will have a solution but an expression will not.
What are the characteristics of a linear expression?
It has a variable.
What does it mean to solve an equation?
It is to find out the value of the equation.
Can an equation have multiple solutions?
No. An equation only has 1 solution.
Can an equation has no solution?
Yes. The answer can be undefined.

8x - 46 = 2
8x=48
x=6

8x + 46 = 2
8x=-44
x=-5.5

-8x +46 = 2
-8x=-44
x=5.5

8x + 46 = 46
8x=0
x=0

8x + 46 = 8x
8x=8x-46

27. 1. 8x - 46 = 2
x = 6
2. 8x + 46 = 2
x = -6
3. -8x +46 = 2
x = 5.5
4. 8x + 46 = 46
x = 0
5. 8x + 46 = 8x
cannot be solved

What is the difference between an equation and an expression?

An equation is a combination of two expressions with an equal sign. Eg. 2x-3=5. However, an expression does not have an equal sign. Eg. 2x

What are the characteristics of a linear expression?

Linear expressions can have more than two expressions and must have at least one variable. Eg, y=3x+4y

What does it mean to solve an equation?

To solve an equation means to simplify it into one or more expressions.

Can an equation have multiple solutions?

No it cannot have multiple solutions.

Can an equation has no solution?

No, it must have a solution, unless the equation is somehow wrong.

1) 8x - 46 = 2
8x=2 +46
x=6

2)8x + 46 = 2
8x=2-46
x=-5.5

3)-8x +46 = 2
-8x=2-46
-x=-44÷8
x=-5.5

4)8x + 46 = 46
8x=46-46
x=0

5)8x + 46 = 8x
8x=8x-46
That is impossible to find as we do not know the value of x. as the two 8x are the same.

1) An equation has a defined answer that can be solved without a variable. An expression can be solved by simplifying, expansion or factorisation that the answer comes out in variables.

2) A linear expression has a term with a variable in it.

3) To solve an equation, we need to find the variable(e.g x) into a number.

4) No. It only can have one answer.

5) Yes. When nothing else can be done if the solution cannot be solved.

1)
8x-46=2
8x =48
48÷8=6
x=6

2)
8x+46=2
8x =-44
x=-5.5

3)
-8x+46 = 2
-8x =-44
x=5.5

4)
8x+46=46
46-46=0
x=0

5)
8x+46=8x
x=undefined variable

Go through the site Study Guides and Strategies and attempt the following questions.

What is the difference between an equation and an expression?
An expression requires us to simplify or factories but not solve while an equation requires us to find a value of a variable.

What are the characteristics of a linear expression?
- Has no operations other than addition, subtraction and multiplication of a variable by a constant
- Variables may not be multiplied together or appear in a denominator
- A linear equation does not contain variable with exponents other than 1
- The graph of a linear equation is always a line

What does it mean to solve an equation?
To find out the value of the variable.

Can an equation have multiple solutions?
No.

Can an equation has no solution?
Yes.

Solve the following equations for the value/s of x.
8x - 46 = 2
8x - 48 = 0
8x = 48
1x= 6

8x + 46 = 2
8x + 44 = 0
8x = -44
1x = -5.5

-8x + 46 = 2
-8x + 44 = 0
-8x = -44
8x = 44
1x = 5.5

8x + 46 = 46
8x + 0 = 0
8x = 0
1x = undefined

8x + 46 = 8x
1x = undefined or infinity

What is the significance of the solutions of the above equations?
They all only have one solution and has no operations other than addition and subtraction.

Can an equation have multiple solutions or no solution? If so, what is the implication.
No.
If the question have an undefined answer, there is no solution to that question.

-Christopher Nah