Solve the inequality algebraically. $$ x^{3}-2 x^{2}-63 x

Question

Solve the inequality algebraically. $$ x^{3}-2 x^{2}-63 x<0 $$ The solution is (Simplify your answer. Type your answer in interval notation. Use integers or fractions for any numbers in the expression.)

UpStudy AI · Accepted Answer

Solve the equation $$ x^{3}-2 x^{2}-63 x<0 $$.
Solve the inequality by following steps:
- step0: Solve the inequality by testing the values in the interval:
  $$x^{3}-2x^{2}-63x<0$$
- step1: Rewrite the expression:
  $$x^{3}-2x^{2}-63x=0$$
- step2: Factor the expression:
  $$x\left(x-9ight)\left(x+7ight)=0$$
- step3: Separate into possible cases:
  $$\begin{align}&x=0\&x-9=0\&x+7=0\end{align}$$
- step4: Solve the equation:
  $$\begin{align}&x=0\&x=9\&x=-7\end{align}$$
- step5: Determine the test intervals:
  $$\begin{align}&x<-7\&-79\end{align}$$
- step6: Choose a value:
  $$\begin{align}&x_{1}=-8\&x_{2}=-4\&x_{3}=5\&x_{4}=10\end{align}$$
- step7: Test the chosen value:
  $$\begin{align}&x<-7	extrm{ }	extrm{is the solution}\&-79	extrm{ }	extrm{is not a solution}\end{align}$$
- step8: The final solution is $$x \in \left(-\infty,-7ight)\cup \left(0,9ight):$$
  $$x \in \left(-\infty,-7ight)\cup \left(0,9ight)$$
The solution to the inequality $$x^{3}-2x^{2}-63x<0$$ is $$x \in (-\infty,-7) \cup (0,9)$$.
$$ x \in (-\infty,-7) \cup (0,9) $$

Solve the inequality algebraically.

The solution is
(Simplify your answer. Type your answer in interval notation. Use integers or fractions for any numbers in
the expression.)

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Solve the inequality algebraically. The solution is (Simplify your answer. Type your answer in interval notation. Use integers or fractions for any numbers in the expression.)