Question

Solve the inequality algebraically.

$x^4<9x^2$

Short answer

The required interval set is :

$(-3,3)$

Step-by-step solution

Step 1. Given inequality 

$x^4<9x^2$

we need to solve for x.

Step 2. Factorization

$$\begin{gathered} x^4-9x^2<0 \\ {x}^2(x^2-9)<0 \\ {x}^2(x+3)(x-3)<0 \end{gathered}$$

The zeros of the given equation are :

$0,3,-3$localid="1646130204622" $0,3,-3$

Step 3. Dividing the number line into 3 intervals 

$$\begin{gathered} (-\infty ,-3) \\ (-3,3) \\ (3,\infty ) \end{gathered}$$

Step 4. Evaluating the value of function at different intervals

3. $(-\infty ,-3)$

let us take the value -4

the value of function at -4

$=112$

2.$(-3,3)$

let us take the number 2

the value of the function at x=2 is :

$=-20$

1. $(3,\infty )$

let us take the value 4

the value of function at x= 4

$=112$

Step 5. Conclusion

The required interval set is :

(-3,3)