Q. 1274.5( 6 Votes )

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

(a) v

(b) w

(c) x

Explain your reasoning using the properties of integers.

Answer :

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.

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