Solve -5x 14>-9x^2

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve the inequality by separating into cases

Solve for x

x \in (- \infty, 0) \cup (\frac{70}{9}, + \infty)

Evaluate

- 5 x \times 14 > - 9 x^{2}

Multiply the terms

- 70 x > - 9 x^{2}

Move the expression to the left side

- 70 x - (- 9 x^{2}) > 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

- 70 x + 9 x^{2} > 0

Rewrite the expression

- 70 x + 9 x^{2} = 0

Factor the expression

More Steps

- x (70 - 9 x) = 0

When the product of factors equals 0,at least one factor is 0

- x = 0 70 - 9 x = 0

Solve the equation for x

x = 0 70 - 9 x = 0

Solve the equation for x

More Steps

x = 0 x = \frac{70}{9}

Determine the test intervals using the critical values

x < 0 0 < x < \frac{70}{9} x > \frac{70}{9}

Choose a value form each interval

x_{1} = - 1 x_{2} = 4 x_{3} = 9

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} = 4 x_{3} = 9

To determine if 0 < x < \frac{70}{9} is the solution to the inequality,test if the chosen value x = 4 satisfies the initial inequality

More Steps

x < 0 is the solution 0 < x < \frac{70}{9} is not a solution x_{3} = 9

To determine if x > \frac{70}{9} is the solution to the inequality,test if the chosen value x = 9 satisfies the initial inequality

More Steps

x < 0 is the solution 0 < x < \frac{70}{9} is not a solution x > \frac{70}{9} is the solution

Solution

x \in (- \infty, 0) \cup (\frac{70}{9}, + \infty)

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