Solve 8x> -3/5 -(-10x^3)

Evaluate

8 x > - \frac{3}{5} - (- 10 x^{3})

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

8 x > - \frac{3}{5} + 10 x^{3}

Move the expression to the left side

8 x - (- \frac{3}{5} + 10 x^{3}) > 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

8 x + \frac{3}{5} - 10 x^{3} > 0

Rewrite the expression

8 x + \frac{3}{5} - 10 x^{3} = 0

Factor the expression

\frac{1}{5} (40 x + 3 - 50 x^{3}) = 0

Divide both sides

40 x + 3 - 50 x^{3} = 0

Calculate

x \approx 0.929801 x \approx - 0.854262 x \approx - 0.075539

Determine the test intervals using the critical values

x < - 0.854262 - 0.854262 < x < - 0.075539 - 0.075539 < x < 0.929801 x > 0.929801

Choose a value form each interval

x_{1} = - 2 x_{2} \approx - 0.464901 x_{3} = 0 x_{4} = 2

To determine if x < - 0.854262 is the solution to the inequality,test if the chosen value x = - 2 satisfies the initial inequality

More Steps

x < - 0.854262 is the solution x_{2} \approx - 0.464901 x_{3} = 0 x_{4} = 2

To determine if - 0.854262 < x < - 0.075539 is the solution to the inequality,test if the chosen value x \approx - 0.464901 satisfies the initial inequality

More Steps

x < - 0.854262 is the solution - 0.854262 < x < - 0.075539 is not a solution x_{3} = 0 x_{4} = 2

To determine if - 0.075539 < x < 0.929801 is the solution to the inequality,test if the chosen value x = 0 satisfies the initial inequality

More Steps

x < - 0.854262 is the solution - 0.854262 < x < - 0.075539 is not a solution - 0.075539 < x < 0.929801 is the solution x_{4} = 2

To determine if x > 0.929801 is the solution to the inequality,test if the chosen value x = 2 satisfies the initial inequality

More Steps

x < - 0.854262 is the solution - 0.854262 < x < - 0.075539 is not a solution - 0.075539 < x < 0.929801 is the solution x > 0.929801 is not a solution

Solution

x \in (- \infty, - 0.854262) \cup (- 0.075539, 0.929801)

Solve the inequality