Solve 3/4-x<5/4x 1/2(2x^3)

Question

Solve the inequality

x \in (- \infty, - 1.103495) \cup (0.594187, + \infty)

Evaluate

\frac{3}{4} - x < \frac{5}{4} x \times \frac{1}{2} \times 2 x^{3}

Multiply

More Steps

\frac{3}{4} - x < \frac{5}{4} x^{4}

Move the expression to the left side

\frac{3}{4} - x - \frac{5}{4} x^{4} < 0

Rewrite the expression

\frac{3}{4} - x - \frac{5}{4} x^{4} = 0

Factor the expression

\frac{1}{4} (3 - 4 x - 5 x^{4}) = 0

Divide both sides

3 - 4 x - 5 x^{4} = 0

Calculate

x \approx - 1.103495 x \approx 0.594187

Determine the test intervals using the critical values

x < - 1.103495 - 1.103495 < x < 0.594187 x > 0.594187

Choose a value form each interval

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

To determine if x < - 1.103495 is the solution to the inequality,test if the chosen value x = - 2 satisfies the initial inequality

More Steps

x < - 1.103495 is the solution x_{2} = 0 x_{3} = 2

To determine if - 1.103495 < x < 0.594187 is the solution to the inequality,test if the chosen value x = 0 satisfies the initial inequality

More Steps

x < - 1.103495 is the solution - 1.103495 < x < 0.594187 is not a solution x_{3} = 2

To determine if x > 0.594187 is the solution to the inequality,test if the chosen value x = 2 satisfies the initial inequality

More Steps

x < - 1.103495 is the solution - 1.103495 < x < 0.594187 is not a solution x > 0.594187 is the solution

Solution

x \in (- \infty, - 1.103495) \cup (0.594187, + \infty)

Show Solution