Solve 5(x-4) x>-7(x^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{5}{3}, + \infty)

Evaluate

5 (x - 4) x > - 7 x^{2}

Multiply the terms

5 x (x - 4) > - 7 x^{2}

Move the expression to the left side

5 x (x - 4) - (- 7 x^{2}) > 0

Subtract the terms

More Steps

12 x^{2} - 20 x > 0

Rewrite the expression

12 x^{2} - 20 x = 0

Factor the expression

More Steps

4 x (3 x - 5) = 0

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

4 x = 0 3 x - 5 = 0

Solve the equation for x

x = 0 3 x - 5 = 0

Solve the equation for x

More Steps

x = 0 x = \frac{5}{3}

Determine the test intervals using the critical values

x < 0 0 < x < \frac{5}{3} x > \frac{5}{3}

Choose a value form each interval

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

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 x_{3} = 3

To determine if 0 < x < \frac{5}{3} is the solution to the inequality,test if the chosen value x = 1 satisfies the initial inequality

More Steps

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

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

More Steps

x < 0 is the solution 0 < x < \frac{5}{3} is not a solution x > \frac{5}{3} is the solution

Solution

x \in (- \infty, 0) \cup (\frac{5}{3}, + \infty)

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