Solve -6> (3x^54)/(-3)

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve for x

x > \frac{5 48}{2}

Alternative Form

x \in (\frac{5 48}{2}, + \infty)

Evaluate

- 6 > \frac{3 x ^{5} \times 4}{- 3}

Reduce the fraction

More Steps

- 6 > - 4 x^{5}

Move the expression to the left side

- 6 - (- 4 x^{5}) > 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

- 6 + 4 x^{5} > 0

Rewrite the expression

- 6 + 4 x^{5} = 0

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

4 x^{5} = 0 + 6

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

4 x^{5} = 6

Divide both sides

\frac{4 x ^{5}}{4} = \frac{6}{4}

Divide the numbers

x^{5} = \frac{6}{4}

Cancel out the common factor 2

x^{5} = \frac{3}{2}

Take the 5 -th root on both sides of the equation

5 x^{5} = 5 \frac{3}{2}

Calculate

x = 5 \frac{3}{2}

Simplify the root

More Steps

x = \frac{5 48}{2}

Determine the test intervals using the critical values

x < \frac{5 48}{2} x > \frac{5 48}{2}

Choose a value form each interval

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

To determine if x < \frac{5 48}{2} is the solution to the inequality,test if the chosen value x = 0 satisfies the initial inequality

More Steps

x < \frac{5 48}{2} is not a solution x_{2} = 2

To determine if x > \frac{5 48}{2} is the solution to the inequality,test if the chosen value x = 2 satisfies the initial inequality

More Steps

x < \frac{5 48}{2} is not a solution x > \frac{5 48}{2} is the solution

Solution

x > \frac{5 48}{2}

Alternative Form

x \in (\frac{5 48}{2}, + \infty)

Show Solution