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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