Solve 4x^5/3 x <3x 1

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve the inequality by separating into cases

0 < x < \frac{5 72}{2}

Alternative Form

x \in (0, \frac{5 72}{2})

Evaluate

(4 \times \frac{x ^{5}}{3}) x < 3 x \times 1

Remove the parentheses

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

Multiply the terms

More Steps

\frac{4 x ^{6}}{3} < 3 x \times 1

Multiply the terms

\frac{4 x ^{6}}{3} < 3 x

Multiply both sides of the inequality by 3

\frac{4 x ^{6}}{3} \times 3 < 3 x \times 3

Multiply the terms

4 x^{6} < 3 x \times 3

Multiply the terms

4 x^{6} < 9 x

Move the expression to the left side

4 x^{6} - 9 x < 0

Rewrite the expression

4 x^{6} - 9 x = 0

Factor the expression

x (4 x^{5} - 9) = 0

Separate the equation into 2 possible cases

x = 0 4 x^{5} - 9 = 0

Solve the equation

More Steps

x = 0 x = \frac{5 72}{2}

Determine the test intervals using the critical values

x < 0 0 < x < \frac{5 72}{2} x > \frac{5 72}{2}

Choose a value form each interval

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

To determine if x < 0 is the solution to the inequality,test if the chosen value x = - 1 satisfies the initial inequality

More Steps

x < 0 is not a solution x_{2} = 1 x_{3} = 2

To determine if 0 < x < \frac{5 72}{2} is the solution to the inequality,test if the chosen value x = 1 satisfies the initial inequality

More Steps

x < 0 is not a solution 0 < x < \frac{5 72}{2} is the solution x_{3} = 2

To determine if x > \frac{5 72}{2} is the solution to the inequality,test if the chosen value x = 2 satisfies the initial inequality

More Steps

x < 0 is not a solution 0 < x < \frac{5 72}{2} is the solution x > \frac{5 72}{2} is not a solution

Solution

0 < x < \frac{5 72}{2}

Alternative Form

x \in (0, \frac{5 72}{2})

Show Solution