Solve -15<12(x^3) 9(-8 x)

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve for x

- \frac{4 360}{12} < x < \frac{4 360}{12}

Alternative Form

x \in (- \frac{4 360}{12}, \frac{4 360}{12})

Evaluate

- 15 < 12 x^{3} \times 9 (- 8 x)

Multiply

More Steps

- 15 < - 864 x^{4}

Move the expression to the left side

- 15 - (- 864 x^{4}) < 0

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

- 15 + 864 x^{4} < 0

Rewrite the expression

- 15 + 864 x^{4} = 0

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

864 x^{4} = 0 + 15

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

864 x^{4} = 15

Divide both sides

\frac{864 x ^{4}}{864} = \frac{15}{864}

Divide the numbers

x^{4} = \frac{15}{864}

Cancel out the common factor 3

x^{4} = \frac{5}{288}

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

x = \pm 4 \frac{5}{288}

Simplify the expression

More Steps

x = \pm \frac{4 360}{12}

Separate the equation into 2 possible cases

x = \frac{4 360}{12} x = - \frac{4 360}{12}

Determine the test intervals using the critical values

x < - \frac{4 360}{12} - \frac{4 360}{12} < x < \frac{4 360}{12} x > \frac{4 360}{12}

Choose a value form each interval

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

To determine if x < - \frac{4 360}{12} is the solution to the inequality,test if the chosen value x = - 1 satisfies the initial inequality

More Steps

x < - \frac{4 360}{12} is not a solution x_{2} = 0 x_{3} = 1

To determine if - \frac{4 360}{12} < x < \frac{4 360}{12} is the solution to the inequality,test if the chosen value x = 0 satisfies the initial inequality

More Steps

x < - \frac{4 360}{12} is not a solution - \frac{4 360}{12} < x < \frac{4 360}{12} is the solution x_{3} = 1

To determine if x > \frac{4 360}{12} is the solution to the inequality,test if the chosen value x = 1 satisfies the initial inequality

More Steps

x < - \frac{4 360}{12} is not a solution - \frac{4 360}{12} < x < \frac{4 360}{12} is the solution x > \frac{4 360}{12} is not a solution

Solution

- \frac{4 360}{12} < x < \frac{4 360}{12}

Alternative Form

x \in (- \frac{4 360}{12}, \frac{4 360}{12})

Show Solution