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**Hint:**We have to firstly consider her age as x. To write an expression for her brother’s age we have to subtract 2 from x. Her father’s age can be obtained adding 32 and x. We can write the expression for her mother’s age by subtracting 5 from her father’s age, that is, $x+32$ . Similarly, her grandfather’s age is obtained by multiplying her age by 8. Finally, to write an expression for her grandmother’s age we have to subtract 4 from 8x.

**Complete step by step answer:**

We have to write an algebraic expression for the given situations. Let us consider her age as x. Now, let us consider each situation.

(a) We are given that her brother is 2 years younger than her. So, we have to subtract 2 from x.

Her brother’s age $=x-2$

(b) We are given that her father’s age exceeds her age by 32 years. This means, we have to add 32 and x.

Her father’s age $=x+32$

(c) We are given that her mother’s age is 5 years less than that of her father. We have to subtract 5 from her father’s age, that is, $x+32$ .

Her mother’s age $=x+32-5$

We have to simplify this expression.

$\Rightarrow $ Her mother’s age $=x+27$

(d) We are given that her grandfather’s age is 8 times her age. This means that we have to multiply her age by 8.

Her grandfather’s age $=8x$

(e) We are given that her grandmother’s age is 4 less than 8 times her age. We have to subtract 4 from 8x.

Her grandmother’s age $=8x-4$

**Note:**Students must always consider the unknown value as x and write the expression accordingly. In algebra, ‘times’ means ‘multiply’. Students have a chance of making a mistake when writing her grandmother’s age as $4-8x$ .

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