Solve x^(2) 4x>77

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve for x

x > \frac{3 154}{2}

Alternative Form

x \in (\frac{3 154}{2}, + \infty)

Evaluate

x^{2} \times 4 x > 77

Multiply

More Steps

4 x^{3} > 77

Move the expression to the left side

4 x^{3} - 77 > 0

Rewrite the expression

4 x^{3} - 77 = 0

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

4 x^{3} = 0 + 77

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

4 x^{3} = 77

Divide both sides

\frac{4 x ^{3}}{4} = \frac{77}{4}

Divide the numbers

x^{3} = \frac{77}{4}

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

3 x^{3} = 3 \frac{77}{4}

Calculate

x = 3 \frac{77}{4}

Simplify the root

More Steps

x = \frac{3 154}{2}

Determine the test intervals using the critical values

x < \frac{3 154}{2} x > \frac{3 154}{2}

Choose a value form each interval

x_{1} = 2 x_{2} = 4

To determine if x < \frac{3 154}{2} is the solution to the inequality,test if the chosen value x = 2 satisfies the initial inequality

More Steps

x < \frac{3 154}{2} is not a solution x_{2} = 4

To determine if x > \frac{3 154}{2} is the solution to the inequality,test if the chosen value x = 4 satisfies the initial inequality

More Steps

x < \frac{3 154}{2} is not a solution x > \frac{3 154}{2} is the solution

Solution

x > \frac{3 154}{2}

Alternative Form

x \in (\frac{3 154}{2}, + \infty)

Show Solution