Solve 4m^6<2 - ScanMath

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve for m

- \frac{6 32}{2} < m < \frac{6 32}{2}

Alternative Form

m \in (- \frac{6 32}{2}, \frac{6 32}{2})

Evaluate

4 m^{6} < 2

Move the expression to the left side

4 m^{6} - 2 < 0

Rewrite the expression

4 m^{6} - 2 = 0

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

4 m^{6} = 0 + 2

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

4 m^{6} = 2

Divide both sides

\frac{4 m ^{6}}{4} = \frac{2}{4}

Divide the numbers

m^{6} = \frac{2}{4}

Cancel out the common factor 2

m^{6} = \frac{1}{2}

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

m = \pm 6 \frac{1}{2}

Simplify the expression

More Steps

m = \pm \frac{6 32}{2}

Separate the equation into 2 possible cases

m = \frac{6 32}{2} m = - \frac{6 32}{2}

Determine the test intervals using the critical values

m < - \frac{6 32}{2} - \frac{6 32}{2} < m < \frac{6 32}{2} m > \frac{6 32}{2}

Choose a value form each interval

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

To determine if m < - \frac{6 32}{2} is the solution to the inequality,test if the chosen value m = - 2 satisfies the initial inequality

More Steps

m < - \frac{6 32}{2} is not a solution m_{2} = 0 m_{3} = 2

To determine if - \frac{6 32}{2} < m < \frac{6 32}{2} is the solution to the inequality,test if the chosen value m = 0 satisfies the initial inequality

More Steps

m < - \frac{6 32}{2} is not a solution - \frac{6 32}{2} < m < \frac{6 32}{2} is the solution m_{3} = 2

To determine if m > \frac{6 32}{2} is the solution to the inequality,test if the chosen value m = 2 satisfies the initial inequality

More Steps

m < - \frac{6 32}{2} is not a solution - \frac{6 32}{2} < m < \frac{6 32}{2} is the solution m > \frac{6 32}{2} is not a solution

Solution

- \frac{6 32}{2} < m < \frac{6 32}{2}

Alternative Form

m \in (- \frac{6 32}{2}, \frac{6 32}{2})

Show Solution