Solve 62>5x^42 - ScanMath

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve for x

- \frac{4 3875}{5} < x < \frac{4 3875}{5}

Alternative Form

x \in (- \frac{4 3875}{5}, \frac{4 3875}{5})

Evaluate

62 > 5 x^{4} \times 2

Multiply the terms

62 > 10 x^{4}

Move the expression to the left side

62 - 10 x^{4} > 0

Rewrite the expression

62 - 10 x^{4} = 0

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

- 10 x^{4} = 0 - 62

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

- 10 x^{4} = - 62

Change the signs on both sides of the equation

10 x^{4} = 62

Divide both sides

\frac{10 x ^{4}}{10} = \frac{62}{10}

Divide the numbers

x^{4} = \frac{62}{10}

Cancel out the common factor 2

x^{4} = \frac{31}{5}

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

x = \pm 4 \frac{31}{5}

Simplify the expression

More Steps

x = \pm \frac{4 3875}{5}

Separate the equation into 2 possible cases

x = \frac{4 3875}{5} x = - \frac{4 3875}{5}

Determine the test intervals using the critical values

x < - \frac{4 3875}{5} - \frac{4 3875}{5} < x < \frac{4 3875}{5} x > \frac{4 3875}{5}

Choose a value form each interval

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

To determine if x < - \frac{4 3875}{5} is the solution to the inequality,test if the chosen value x = - 3 satisfies the initial inequality

More Steps

x < - \frac{4 3875}{5} is not a solution x_{2} = 0 x_{3} = 3

To determine if - \frac{4 3875}{5} < x < \frac{4 3875}{5} is the solution to the inequality,test if the chosen value x = 0 satisfies the initial inequality

More Steps

x < - \frac{4 3875}{5} is not a solution - \frac{4 3875}{5} < x < \frac{4 3875}{5} is the solution x_{3} = 3

To determine if x > \frac{4 3875}{5} is the solution to the inequality,test if the chosen value x = 3 satisfies the initial inequality

More Steps

x < - \frac{4 3875}{5} is not a solution - \frac{4 3875}{5} < x < \frac{4 3875}{5} is the solution x > \frac{4 3875}{5} is not a solution

Solution

- \frac{4 3875}{5} < x < \frac{4 3875}{5}

Alternative Form

x \in (- \frac{4 3875}{5}, \frac{4 3875}{5})

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