Solve (-9x^2)4(-5x-9)2≥0

Question

Solve the inequality

x \geq - \frac{9}{5}

Alternative Form

x \in [- \frac{9}{5}, + \infty)

Evaluate

(- 9 x^{2}) \times 4 (- 5 x - 9) \times 2 \geq 0

Remove the parentheses

- 9 x^{2} \times 4 (- 5 x - 9) \times 2 \geq 0

Multiply the terms

More Steps

- 72 x^{2} (- 5 x - 9) \geq 0

Change the signs on both sides of the inequality and flip the inequality sign

72 x^{2} (- 5 x - 9) \leq 0

Rewrite the expression

72 x^{2} (- 5 x - 9) = 0

Elimination the left coefficient

x^{2} (- 5 x - 9) = 0

Separate the equation into 2 possible cases

x^{2} = 0 - 5 x - 9 = 0

The only way a power can be 0 is when the base equals 0

x = 0 - 5 x - 9 = 0

Solve the equation

More Steps

x = 0 x = - \frac{9}{5}

Determine the test intervals using the critical values

x < - \frac{9}{5} - \frac{9}{5} < x < 0 x > 0

Choose a value form each interval

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

To determine if x < - \frac{9}{5} is the solution to the inequality,test if the chosen value x = - 3 satisfies the initial inequality

More Steps

x < - \frac{9}{5} is not a solution x_{2} = - 1 x_{3} = 1

To determine if - \frac{9}{5} < x < 0 is the solution to the inequality,test if the chosen value x = - 1 satisfies the initial inequality

More Steps

x < - \frac{9}{5} is not a solution - \frac{9}{5} < x < 0 is the solution x_{3} = 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 < - \frac{9}{5} is not a solution - \frac{9}{5} < x < 0 is the solution x > 0 is the solution

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

- \frac{9}{5} \leq x \leq 0 is the solution x \geq 0 is the solution

Solution

x \geq - \frac{9}{5}

Alternative Form

x \in [- \frac{9}{5}, + \infty)

Show Solution