Solve (x 1)(x^2)(x^3)(x^4)<=120

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve for x

- 10120 \leq x \leq 10120

Alternative Form

x \in [- 10120, 10120]

Evaluate

(x \times 1) x^{2} \times x^{3} \times x^{4} \leq 120

Remove the parentheses

x \times 1 \times x^{2} \times x^{3} \times x^{4} \leq 120

Multiply the terms

More Steps

x^{10} \leq 120

Move the expression to the left side

x^{10} - 120 \leq 0

Rewrite the expression

x^{10} - 120 = 0

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

x^{10} = 0 + 120

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

x^{10} = 120

Take the root of both sides of the equation and remember to use both positive and negative roots

x = \pm 10120

Separate the equation into 2 possible cases

x = 10120 x = - 10120

Determine the test intervals using the critical values

x < - 10120 - 10120 < x < 10120 x > 10120

Choose a value form each interval

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

To determine if x < - 10120 is the solution to the inequality,test if the chosen value x = - 3 satisfies the initial inequality

More Steps

x < - 10120 is not a solution x_{2} = 0 x_{3} = 3

To determine if - 10120 < x < 10120 is the solution to the inequality,test if the chosen value x = 0 satisfies the initial inequality

More Steps

x < - 10120 is not a solution - 10120 < x < 10120 is the solution x_{3} = 3

To determine if x > 10120 is the solution to the inequality,test if the chosen value x = 3 satisfies the initial inequality

More Steps

x < - 10120 is not a solution - 10120 < x < 10120 is the solution x > 10120 is not a solution

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

- 10120 \leq x \leq 10120 is the solution

Solution

- 10120 \leq x \leq 10120

Alternative Form

x \in [- 10120, 10120]

Show Solution