## Monday, July 5, 2010

### 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.

In this task review the view clip again on how ' x finds out his value'.

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?
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.

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

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

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

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

8x + 46 = 8x
8x -8x = -46
0 = -46
x = ∞ (undefined)
What is the significance of the solutions of the above equations?
Ans: It is the value of the variables.

Can an equation have multiple solutions or no solution? If so, what is the implication.
Ans: Yes, they can. The answer for the equation can have many different values or there is no defined value. Such cases like this can be found in examples like equation 5(above). In these situations, we can leave the answer as ∞ or undefined.

Done by: See To, Niklaus, Rayner

2. 1.8x - 46 = 2
8x = 2+46
x = 6
2.8x + 46 = 2
8x = -44
x = -5.5
3.-8x +46 = 2
-8x = 2+46
x = -6
4.8x + 46 = 46
8x = 0
x = ∞ Undefined
5.8x + 46 = 8x
8x-8x = -46
x = ∞ Undefined

What is the significance of the solutions of the above equations?
Balance the equation.
Can an equation have multiple solutions or no solution? If so, what is the implication.
Yes, an equation can have multiple solutions but the solutions may be rather confusing.

a) A mathematical expression has an equal sign with linear expressions while a mathematical equation performs functions of addition, subtraction, multiplication, and division.

b) A linear expression cannot have components or powers, it cannot multiply or divide each other, and it cannot be found under a square/root sign.

c) To solve an equation is to find what values (numbers, functions, sets, etc.) fulfill a condition stated in the form of an equation (two expressions related byequality). These expressions contain one or more variables which values are sought that cause the condition to be fulfilled.

d) Yes, it can.

Preston, Michelle, Jia Le

1. An linear equation is a mathematical expression that has an equal sign and linear expressions while a linear expression is a mathematical statement that performs functions of addition, subtraction, multiplication, and division.
2. A linear expression cannot have exponents (or powers). A linear expression cannot multiply or divide each other. A linear expression cannot be found under a root sign or square root sign (sqrt).
3. Solve these linear equations by dragging a number to the "other" side of the equal sign.
Remember that you are "isolating" the unknown "X" to solve the problem.
4. Yes.

5. a.)An equation is a sentence
One solves an equation.
An equation has a relation symbol.
An expression is a phrase , a sentence fragment.
One simplifies an expression.
An expression has no relation symbol.
b.) The characteristic of linear expression is that they cannot have components or powers, it cannot multiply or divide each other, and it cannot be found under a square/root sign.
c)Isolating the unknown variable to discover its value.
d) Yes.

Done By : Johanan and Tim

8x - 46 = 2
8x=2+46
x=6
8x + 46 = 2
8x=2-46
x=44/8
x=11/2
-8x +46 = 2
-8x=2-46
-8x=-44
8x=44
x=11/2
8x + 46 = 46
8x=46-46
8x=0
x=0
8x + 46 = 8x
8x-8x=-46
0x=-46

What is the significance of the solutions of the above equations?
-The significance of the solutions of the above equations is that the operations in front of the numbers affect the answer.
Can an equation have multiple solutions or no solution? If so, what is the implication.
-Yes, it can. If It has no solution, then we can’t solve it. If it has many solutions, we can take any value of x.

Done by: Benjamin, Jun Wei and Naveena

a. An equation is a mathematical expression that has an equal sign and linear expressions and an expression is a mathematical statement that performs functions of addition, subtraction, multiplication, and division.

b. Linear expression does not have powers [like a³], does not multiply or divide 2 variables [b multiplied by x] , does not have a square root [like square root of n]

c. To solve an equation, you must find the value(s) that can be substituted in for all the variables that will maintain the accuracy of the equation. In simpler terms, you must find the values of all the variables.
For example, to solve x + 3 = 5 you must determine which value(s) can be substituted for x that will maintain the equation. To do this:
x + 3 (- 3) = 5 (- 3)
x = 2.
So the solution to that equation is x = 2.

d. Yes. For example, if 0 x y.

Done by: YuChong, Cherin and Min Suk

8. Task 3: Stacey, Victor, Si Yuan

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

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

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

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

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

A. Different expressions have different solutions, which have different answers.
B. Yes, an equation can have multiple solution or no solution.

9. My comment:
3.4.8x + 46 = 46
8x = 0
x = 0

10. Task 3-Done by: Benjamin, Jun Wei, Naveena
8x + 46 = 8x
8x-8x=-46
0x=-46
x=Undefined

11. I am referring to Jun Hong's post. The comments were very well done and very explanatory. Very detailed.

Preston

12. I am referring to Jun Hong's post. The comments are to the point and detailed.