Solve 15x-3x 1-5x 115-x^22x≥0

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

15 x - 3 x \times 1 - 5 x \times 115 - x^{2} \times 2 x \geq 0

Simplify

More Steps

- 563 x - 2 x^{3} \geq 0

Rewrite the expression

- 563 x - 2 x^{3} = 0

Factor the expression

- x (563 + 2 x^{2}) = 0

Divide both sides

x (563 + 2 x^{2}) = 0

Separate the equation into 2 possible cases

x = 0 563 + 2 x^{2} = 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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