IP3U2 HOT PN1 Q3

IP3U2 HOT PN1 Q3

IP 3

Solve each of the following inequalities.

  1. \(\frac{{{\alpha }^{2}}+2}{\alpha -1}<0\)
  2. \(\frac{{{\alpha }^{2}}-4}{\alpha }>0\)
  3. \(\left( x+4 \right)\left( 2x-1 \right)\left( x-3 \right)\ge 0\)
  4. \(\left( 2x+3 \right)\left( x-1 \right)\left( 2-x \right)<0\)
  5. \(\frac{\left( 3x+4 \right)\left( x-5 \right)}{2x-1}\ge 0\)

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Answer:(a) \(\alpha<1\) (b) \(-2<\alpha<0\) or \(\alpha>2\) (c) \(-4\le x\le\frac12\) or \(x\ge3\) (d) \(-\frac32<x<1\) or \(x>2\) (e) \(-\frac43\le x<\frac12\) or \(x\ge5\)

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