We know that Algebra is all about of variables. Algebra involves addition, subtraction, multiplication, and division of variables.
First of all, we must know
What the variable is in Algebra?
Well, variable refers to anything that can have changeable attribute and its attribute can be changed according to need. Similarly, we use some letters like x, y, z etc in algebra whose value can be assumed to be any number.
Their value is not constant but it differs from problem to problem.
For example in the equation x+5=7, the value of x is 2 since 2+5=7
But on the other hand in the equation x-9=5, the value of x is 14 since 14-9=5
Therefore, we can observe that a variable has not a static value but its value varies with problem to problem.
Problems for practice-
Identify the variables in the following algebraic expressions:
(a) x+5
(b) 6z+8
(c) 9+5+2y
(d) x+y+𝛑
(e) $\frac{x^2}{5}$
I hope by doing the above problems, you will have become aware of the variables.
Let's try to use variables in some of the mathematical problems.
For example, If John has some dollars and he spent 7 dollars on his stationery. He counts the money with him and finds that he has 9 dollars. How many dollars had he initially?
Solution: In this problem, we don't know the amount that John had initially.
We always assume unknown number to be a variable.
Here, the unknown number is the amount that John had initially and it is the variable. We can represent it by x, y, z etc.
Therefore, we can say that John had x dollars initially.
To solve this problem, the second step is to form a mathematical model for the given problem.
Since he spent $7. This amount must be subtracted from the amount x to get the balance amount with him.
Let's subtract 7 from x we get x-7
and this difference must be equal to 9, the amount that John finally had.
Hence, we can write x-7=9
This is the required mathematical model for the above-given problem.
Problems for practice-
Identify the variables in the following algebraic expressions:
(a) x+5
(b) 6z+8
(c) 9+5+2y
(d) x+y+𝛑
(e) $\frac{x^2}{5}$
I hope by doing the above problems, you will have become aware of the variables.
Let's try to use variables in some of the mathematical problems.
For example, If John has some dollars and he spent 7 dollars on his stationery. He counts the money with him and finds that he has 9 dollars. How many dollars had he initially?
Solution: In this problem, we don't know the amount that John had initially.
We always assume unknown number to be a variable.
Here, the unknown number is the amount that John had initially and it is the variable. We can represent it by x, y, z etc.
Therefore, we can say that John had x dollars initially.
To solve this problem, the second step is to form a mathematical model for the given problem.
Since he spent $7. This amount must be subtracted from the amount x to get the balance amount with him.
Let's subtract 7 from x we get x-7
and this difference must be equal to 9, the amount that John finally had.
Hence, we can write x-7=9
This is the required mathematical model for the above-given problem.
Now try this?
Write the mathematical models for the given problems
(a) Two times a number is subtracted from 50, we get 20
(b) Adding 12 to 3 times a number, we get 57
(c) The length of a rectangle is 2.5 times its width. Find an expression for the area of the rectangle.
We will do some more concepts in the next post.
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