Solve |3a^6|<4 - ScanMath

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve for a

- \frac{6 972}{3} < a < \frac{6 972}{3}

Alternative Form

a \in (- \frac{6 972}{3}, \frac{6 972}{3})

Evaluate

3 a^{6} < 4

Calculate the absolute value

More Steps

3 a^{6} < 4

Move the expression to the left side

3 a^{6} - 4 < 0

Rewrite the expression

3 a^{6} - 4 = 0

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

3 a^{6} = 0 + 4

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

3 a^{6} = 4

Divide both sides

\frac{3 a ^{6}}{3} = \frac{4}{3}

Divide the numbers

a^{6} = \frac{4}{3}

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

a = \pm 6 \frac{4}{3}

Simplify the expression

More Steps

a = \pm \frac{6 972}{3}

Separate the equation into 2 possible cases

a = \frac{6 972}{3} a = - \frac{6 972}{3}

Determine the test intervals using the critical values

a < - \frac{6 972}{3} - \frac{6 972}{3} < a < \frac{6 972}{3} a > \frac{6 972}{3}

Choose a value form each interval

a_{1} = - 2 a_{2} = 0 a_{3} = 2

To determine if a < - \frac{6 972}{3} is the solution to the inequality,test if the chosen value a = - 2 satisfies the initial inequality

More Steps

a < - \frac{6 972}{3} is not a solution a_{2} = 0 a_{3} = 2

To determine if - \frac{6 972}{3} < a < \frac{6 972}{3} is the solution to the inequality,test if the chosen value a = 0 satisfies the initial inequality

More Steps

a < - \frac{6 972}{3} is not a solution - \frac{6 972}{3} < a < \frac{6 972}{3} is the solution a_{3} = 2

To determine if a > \frac{6 972}{3} is the solution to the inequality,test if the chosen value a = 2 satisfies the initial inequality

More Steps

a < - \frac{6 972}{3} is not a solution - \frac{6 972}{3} < a < \frac{6 972}{3} is the solution a > \frac{6 972}{3} is not a solution

Solution

- \frac{6 972}{3} < a < \frac{6 972}{3}

Alternative Form

a \in (- \frac{6 972}{3}, \frac{6 972}{3})

Show Solution