Solve h*h^310<6 - ScanMath

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve for h

- \frac{4 375}{5} < h < \frac{4 375}{5}

Alternative Form

h \in (- \frac{4 375}{5}, \frac{4 375}{5})

Evaluate

h \times h^{3} \times 10 < 6

Multiply

More Steps

10 h^{4} < 6

Move the expression to the left side

10 h^{4} - 6 < 0

Rewrite the expression

10 h^{4} - 6 = 0

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

10 h^{4} = 0 + 6

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

10 h^{4} = 6

Divide both sides

\frac{10 h ^{4}}{10} = \frac{6}{10}

Divide the numbers

h^{4} = \frac{6}{10}

Cancel out the common factor 2

h^{4} = \frac{3}{5}

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

h = \pm 4 \frac{3}{5}

Simplify the expression

More Steps

h = \pm \frac{4 375}{5}

Separate the equation into 2 possible cases

h = \frac{4 375}{5} h = - \frac{4 375}{5}

Determine the test intervals using the critical values

h < - \frac{4 375}{5} - \frac{4 375}{5} < h < \frac{4 375}{5} h > \frac{4 375}{5}

Choose a value form each interval

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

To determine if h < - \frac{4 375}{5} is the solution to the inequality,test if the chosen value h = - 2 satisfies the initial inequality

More Steps

h < - \frac{4 375}{5} is not a solution h_{2} = 0 h_{3} = 2

To determine if - \frac{4 375}{5} < h < \frac{4 375}{5} is the solution to the inequality,test if the chosen value h = 0 satisfies the initial inequality

More Steps

h < - \frac{4 375}{5} is not a solution - \frac{4 375}{5} < h < \frac{4 375}{5} is the solution h_{3} = 2

To determine if h > \frac{4 375}{5} is the solution to the inequality,test if the chosen value h = 2 satisfies the initial inequality

More Steps

h < - \frac{4 375}{5} is not a solution - \frac{4 375}{5} < h < \frac{4 375}{5} is the solution h > \frac{4 375}{5} is not a solution

Solution

- \frac{4 375}{5} < h < \frac{4 375}{5}

Alternative Form

h \in (- \frac{4 375}{5}, \frac{4 375}{5})

Show Solution