Solve \left(4x^2\right)<3^{6}

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve the inequality by separating into cases

Solve for x

- \frac{27}{2} < x < \frac{27}{2}

Alternative Form

x \in (- \frac{27}{2}, \frac{27}{2})

Evaluate

4 x^{2} < 3^{6}

Move the expression to the left side

4 x^{2} - 3^{6} < 0

Evaluate the power

4 x^{2} - 729 < 0

Rewrite the expression

4 x^{2} - 729 = 0

Move the constant to the right-hand side and change its sign

4 x^{2} = 0 + 729

Removing 0 doesn't change the value,so remove it from the expression

4 x^{2} = 729

Divide both sides

\frac{4 x ^{2}}{4} = \frac{729}{4}

Divide the numbers

x^{2} = \frac{729}{4}

Take the root of both sides of the equation and remember to use both positive and negative roots

x = \pm \frac{729}{4}

Simplify the expression

More Steps

x = \pm \frac{27}{2}

Separate the equation into 2 possible cases

x = \frac{27}{2} x = - \frac{27}{2}

Determine the test intervals using the critical values

x < - \frac{27}{2} - \frac{27}{2} < x < \frac{27}{2} x > \frac{27}{2}

Choose a value form each interval

x_{1} = - 15 x_{2} = 0 x_{3} = 15

To determine if x < - \frac{27}{2} is the solution to the inequality,test if the chosen value x = - 15 satisfies the initial inequality

More Steps

x < - \frac{27}{2} is not a solution x_{2} = 0 x_{3} = 15

To determine if - \frac{27}{2} < x < \frac{27}{2} is the solution to the inequality,test if the chosen value x = 0 satisfies the initial inequality

More Steps

x < - \frac{27}{2} is not a solution - \frac{27}{2} < x < \frac{27}{2} is the solution x_{3} = 15

To determine if x > \frac{27}{2} is the solution to the inequality,test if the chosen value x = 15 satisfies the initial inequality

More Steps

x < - \frac{27}{2} is not a solution - \frac{27}{2} < x < \frac{27}{2} is the solution x > \frac{27}{2} is not a solution

Solution

- \frac{27}{2} < x < \frac{27}{2}

Alternative Form

x \in (- \frac{27}{2}, \frac{27}{2})

Show Solution