Solve 14x115x^2 <= 500

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve for x

x \leq \frac{3 1296050}{161}

Alternative Form

x \in (- \infty, \frac{3 1296050}{161}]

Evaluate

14 x \times 115 x^{2} \leq 500

Multiply

More Steps

1610 x^{3} \leq 500

Move the expression to the left side

1610 x^{3} - 500 \leq 0

Rewrite the expression

1610 x^{3} - 500 = 0

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

1610 x^{3} = 0 + 500

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

1610 x^{3} = 500

Divide both sides

\frac{1610 x ^{3}}{1610} = \frac{500}{1610}

Divide the numbers

x^{3} = \frac{500}{1610}

Cancel out the common factor 10

x^{3} = \frac{50}{161}

Take the 3 -th root on both sides of the equation

3 x^{3} = 3 \frac{50}{161}

Calculate

x = 3 \frac{50}{161}

Simplify the root

More Steps

x = \frac{3 1296050}{161}

Determine the test intervals using the critical values

x < \frac{3 1296050}{161} x > \frac{3 1296050}{161}

Choose a value form each interval

x_{1} = 0 x_{2} = 2

To determine if x < \frac{3 1296050}{161} is the solution to the inequality,test if the chosen value x = 0 satisfies the initial inequality

More Steps

x < \frac{3 1296050}{161} is the solution x_{2} = 2

To determine if x > \frac{3 1296050}{161} is the solution to the inequality,test if the chosen value x = 2 satisfies the initial inequality

More Steps

x < \frac{3 1296050}{161} is the solution x > \frac{3 1296050}{161} is not a solution

The original inequality is a nonstrict inequality,so include the critical value in the solution

x \leq \frac{3 1296050}{161} is the solution

Solution

x \leq \frac{3 1296050}{161}

Alternative Form

x \in (- \infty, \frac{3 1296050}{161}]

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