Additional Mathematics – Equations, inequalities and graphs | e-Consult
Equations, inequalities and graphs (1 questions)
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Answer 2
First rewrite the inequality as \( (2x-4)(x+1)(x-5) - 2
The zeros of \(g(x)\) are approximately \(x\approx -1.24,\;1.00,\;4.24\) (found by solving \(g(x)=0\)).
Sign analysis of \(g(x)\):
- \((-\infty,-1.24):\;g(x)
- \((-1.24,1.00):\;g(x)>0\)
- \((1.00,4.24):\;g(x)
- \((4.24,\infty):\;g(x)>0\)
Thus \(g(x)
\[(-\infty,-1.24)\cup(1.00,4.24)\]