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Below u, v, w and x represent different integers, where u = –4 and x ≠ 1. By using following equations, find each of the values:

u × v = u

x × w = w

u + x = w

- v
- w
- x

Explain your reasoning using the properties of integers.

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#### Solution

We have, three equations

u × v = u ......(i)

x × w = w ......(ii)

u + x = w ......(iii)

and u = –4

**a.** By putting the value of u in equation (i), we get

(–4) × v = (–4)

⇒ v = `((-4))/((-4))`

⇒ v = 1

**b.** From equation (ii),

x × w = w

⇒ x = `w/w`

⇒ v = 1

But, Hence x × w = w, (ii) is possible, when w = 0 (x ≠ 1).

**c.** From equation (iii), u + x = w

Put u = –4 and w = 0, we get

⇒ –4 + x = 0

⇒ x = 4

∴ v = 1, x = 4 and w = 0.

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