# Expressions with Variables

## Notes

### Expressions with Variables:

These expressions are formed from numbers like 2, 3, 4, 10, 100, and so on. To form expressions we use all the four number operations of addition, subtraction, multiplication, and division.
For example, to form (2 × 10) + 3, we have multiplied 2 by 10 and then added 3 to the product.

Examples of some of the other arithmetic expressions are (– 3 × 40) + 5, (5 × 7) – (3 × 4 – 7), etc.

We know that variables can take different values; they have no fixed value. But they are numbers. That is why as in the case of numbers, operations of addition, subtraction, multiplication, and division can be done on them.

One important point must be noted regarding the expressions containing variables. A number expression like (4 × 3) + 5 can be immediately evaluated as (4 × 3) + 5 = 12 + 5 = 17

But an expression like (4x + 5), which contains the variable x, cannot be evaluated. Only if x is given some value, an expression like (4x + 5) can be evaluated. For example, when x = 3, 4x + 5 = (4 × 3) + 5 = 17 as found above.

### How formed?

3 x + 2 first x multiplied by 3, then 2 added to the product
– 5 q q multiplied by –5
y multiplied by 10 and then 7 added to the product 10 y + 7
n multiplied by 2 and 1 subtracted from the product 2 n – 1
y divided by 8 y/8

### Statements using ordinary language)

1. Sarita has 10 more marbles than Ameena. Let Ameena have x marbles. Sarita has (x + 10) marbles.
2. Balu is 3 years younger than Raju. Let Raju’s age be x years. Balu’s age is (x - 3) years.
3. Bikash is twice as old as Raju. Let Raju’s age be x years. Bikash’s age is 2x years.
4. Raju’s father’s age is 2 years more than 3 times Raju’s age. Let Raju’s age be x years. Raju’s father’s age is (3x + 2) years.
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To Tell How The Given Algebraic Expressions Have Been Formed [00:04:59]
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