Question

(problem occurred last time) solve the following inequality algebraically andinclude an interval chart/table:3x^2(x^2-8) + 6x + 5 < 4x^4 - 6x(4x-1) + 4

Answer 1

Simplify the given inequality as shown below

$\begin{gathered} 3x^2(x^2-8)+6x+5<4x^4-6x(4x-1)+4 \\ \Rightarrow3x^4-24x^2+6x+5<4x^4-24x^2+6x+4 \\ \Rightarrow4x^4-24x^2+6x+4-(3x^2-24x^2+6x+5)>0 \end{gathered}$$\begin{gathered} \Rightarrow x^4-1>0 \\ \Rightarrow x^4>1 \end{gathered}$

Suppose that x is a real number; then, the inequality is satisfied for the intervals described in the table below

Therefore, the solution to the inequality in interval notation is

$x\in(-\infty,1)\cup(1,\infty)$