127. Let \(u,v,w,x\) be integers with \(u=-4\) and \(x\neq1\). Given
\(u\times v = u\), \(x\times w = w\), \(u + x = w\).
Find (a) \(v\), (b) \(w\), (c) \(x\).
(a) 1
(b) 0
(c) 4
From \(u\times v=u\) with \(u\neq0\) ⇒ \(v=1\). From \(x\times w=w\) ⇒ \(w( x−1)=0\). Since \(x\neq1\), \(w=0\). Then \(u+x=w\Rightarrow −4+x=0\Rightarrow x=4\).