# 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 = ux × w = wu + x = w(a) v(b) w(c) xExplain your reasoning using the properties of integers.

Given are four variables u, v, w and x representing different integers.

Also, given that there are three equations:

u × v = u …(i)

x × w = w …(ii)

u + x = w …(iii)

Given that, u = -4 and x ≠ 1.

(a). To find: v

Use equation (i), we have

u × v = u

v = 1 [u in numerator cancels out u in denominator]

Thus, v = 1.

(b). To find: w

Use equation (ii) to proceed to find w.

We have

x × w = w

x = 1

But, x ≠ 1 according to the question.

So, we don’t have any choice but to put w = 0 so that x ≠ 1.

Thus, w = 0

(c). To find: x

Use equation (iii) to find x, we have

u + x = w

(-4) + x = 0 [u = -4 is given in the question]

x = 0 + 4

x = 4

Thus, x = 4.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.