Solve 3x^5≤-7x 8

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve the inequality by separating into cases

x \leq 0

Alternative Form

x \in (- \infty, 0]

Evaluate

3 x^{5} \leq - 7 x \times 8

Multiply the terms

3 x^{5} \leq - 56 x

Move the expression to the left side

3 x^{5} - (- 56 x) \leq 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

3 x^{5} + 56 x \leq 0

Rewrite the expression

3 x^{5} + 56 x = 0

Factor the expression

x (3 x^{4} + 56) = 0

Separate the equation into 2 possible cases

x = 0 3 x^{4} + 56 = 0

Solve the equation

More Steps

x = 0 x \in / R

Find the union

x = 0

Determine the test intervals using the critical values

x < 0 x > 0

Choose a value form each interval

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

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 the solution x_{2} = 1

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 the solution x > 0 is not a solution

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

x \leq 0 is the solution

Solution

x \leq 0

Alternative Form

x \in (- \infty, 0]

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