Solve 4x^4\leq9x 8

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve the inequality by separating into cases

0 \leq x \leq 318

Alternative Form

x \in [0, 318]

Evaluate

4 x^{4} \leq 9 x \times 8

Multiply the terms

4 x^{4} \leq 72 x

Move the expression to the left side

4 x^{4} - 72 x \leq 0

Rewrite the expression

4 x^{4} - 72 x = 0

Factor the expression

4 x (x^{3} - 18) = 0

Divide both sides

x (x^{3} - 18) = 0

Separate the equation into 2 possible cases

x = 0 x^{3} - 18 = 0

Solve the equation

More Steps

x = 0 x = 318

Determine the test intervals using the critical values

x < 0 0 < x < 318 x > 318

Choose a value form each interval

x_{1} = - 1 x_{2} = 1 x_{3} = 4

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} = 4

To determine if 0 < x < 318 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 < 318 is the solution x_{3} = 4

To determine if x > 318 is the solution to the inequality,test if the chosen value x = 4 satisfies the initial inequality

More Steps

x < 0 is not a solution 0 < x < 318 is the solution x > 318 is not a solution

The original inequality is a nonstrict inequality,so include the critical value in the solution

0 \leq x \leq 318 is the solution

Solution

0 \leq x \leq 318

Alternative Form

x \in [0, 318]

Show Solution