Solution:
Meera's present age is [tex]x[/tex] years.
1. Meera's age 5 years from now is [tex](x + 5)[/tex] years.
2. Meera's age 3 years ago was [tex](x - 3)[/tex] years.
3. Meera's grandfather's age is [tex]6x[/tex] years.
4. Meera's grandmother's age is [tex](6x - 2)[/tex] years.
5. Meera's father's age is [tex](3x + 5)[/tex] years.

Example 12:
Change the following statement using expressions in a statement language:
"Given Salim scores [tex]r[/tex] runs in a cricket match. Nalin scores [tex](r + 15)[/tex] runs."
Solution:
In a cricket match, Nalin scores 15 more runs than Salim.

Exercise 9.3:
1. Write all the terms of each of the following algebraic expressions:
i. [tex]3 - 7x[/tex]
ii. [tex]2 - 5a + \frac{3}{2}b[/tex]
iii. [tex]3x^5 + 4y^3 - 7xy^2 + 3[/tex]
iv. [tex]2x^2 - \frac{3}{x} + \frac{5}{x^2} + 9[/tex]

Question

27-07-2024
Mathematics

Answered

Solution:
Meera's present age is [tex]x[/tex] years.
1. Meera's age 5 years from now is [tex](x + 5)[/tex] years.
2. Meera's age 3 years ago was [tex](x - 3)[/tex] years.
3. Meera's grandfather's age is [tex]6x[/tex] years.
4. Meera's grandmother's age is [tex](6x - 2)[/tex] years.
5. Meera's father's age is [tex](3x + 5)[/tex] years.

Example 12:
Change the following statement using expressions in a statement language:
"Given Salim scores [tex]r[/tex] runs in a cricket match. Nalin scores [tex](r + 15)[/tex] runs."
Solution:
In a cricket match, Nalin scores 15 more runs than Salim.

Exercise 9.3:
1. Write all the terms of each of the following algebraic expressions:
i. [tex]3 - 7x[/tex]
ii. [tex]2 - 5a + \frac{3}{2}b[/tex]
iii. [tex]3x^5 + 4y^3 - 7xy^2 + 3[/tex]
iv. [tex]2x^2 - \frac{3}{x} + \frac{5}{x^2} + 9[/tex]

Answer :

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GinnyAnswer GinnyAnswer · Answer 1 · 2024-07-27T13:14:07-04:00

Let's address Exercise 9.3 by breaking down each algebraic expression into its individual terms.

### (i) [tex]$3 - 7x$[/tex]
This expression has two terms:
- The constant term: [tex]$3$[/tex]
- The term involving [tex]$x$[/tex]: [tex]$-7x$[/tex]

Thus, the terms of the expression [tex]$3 - 7x$[/tex] are:
- [tex]$3$[/tex]
- [tex]$-7x$[/tex]

### (ii) [tex]$2 - 5a + \frac{3}{2}b$[/tex]
This expression has three terms:
- The constant term: [tex]$2$[/tex]
- The term involving [tex]$a$[/tex]: [tex]$-5a$[/tex]
- The term involving [tex]$b$[/tex]: [tex]$\frac{3}{2}b$[/tex]

Thus, the terms of the expression [tex]$2 - 5a + \frac{3}{2}b$[/tex] are:
- [tex]$2$[/tex]
- [tex]$-5a$[/tex]
- [tex]$\frac{3}{2}b$[/tex]

### (iii) [tex]$3x^5 + 4y^3 - 7xy^2 + 3$[/tex]
This expression has four terms:
- The term involving [tex]$x^5$[/tex]: [tex]$3x^5$[/tex]
- The term involving [tex]$y^3$[/tex]: [tex]$4y^3$[/tex]
- The term involving both [tex]$x$[/tex] and [tex]$y^2$[/tex]: [tex]$-7xy^2$[/tex]
- The constant term: [tex]$3$[/tex]

Thus, the terms of the expression [tex]$3x^5 + 4y^3 - 7xy^2 + 3$[/tex] are:
- [tex]$3x^5$[/tex]
- [tex]$4y^3$[/tex]
- [tex]$-7xy^2$[/tex]
- [tex]$3$[/tex]

### (iv) [tex]$2x^2 - \frac{3}{x} + \frac{5}{x^2} + 9$[/tex]
This expression has four terms:
- The term involving [tex]$x^2$[/tex]: [tex]$2x^2$[/tex]
- The term involving [tex]$x$[/tex] in the denominator: [tex]$-\frac{3}{x}$[/tex]
- The term involving [tex]$x^2$[/tex] in the denominator: [tex]$\frac{5}{x^2}$[/tex]
- The constant term: [tex]$9$[/tex]

Thus, the terms of the expression [tex]$2x^2 - \frac{3}{x} + \frac{5}{x^2} + 9$[/tex] are:
- [tex]$2x^2$[/tex]
- [tex]$-\frac{3}{x}$[/tex]
- [tex]$\frac{5}{x^2}$[/tex]
- [tex]$9$[/tex]

In summary:
1. The terms of [tex]$3 - 7x$[/tex] are [tex]$3$[/tex] and [tex]$-7x$[/tex].
2. The terms of [tex]$2 - 5a + \frac{3}{2}b$[/tex] are [tex]$2$[/tex], [tex]$-5a$[/tex], and [tex]$\frac{3}{2}b$[/tex].
3. The terms of [tex]$3x^5 + 4y^3 - 7xy^2 + 3$[/tex] are [tex]$3x^5$[/tex], [tex]$4y^3$[/tex], [tex]$-7xy^2$[/tex], and [tex]$3$[/tex].
4. The terms of [tex]$2x^2 - \frac{3}{x} + \frac{5}{x^2} + 9$[/tex] are [tex]$2x^2$[/tex], [tex]$-\frac{3}{x}$[/tex], [tex]$\frac{5}{x^2}$[/tex], and [tex]$9$[/tex].