Solve -2x^2 - 7x < 0 - Socratic AI (ScanMath)

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, - \frac{7}{2}) \cup (0, + \infty)

Evaluate

- 2 x^{2} - 7 x < 0

Rewrite the expression

- 2 x^{2} - 7 x = 0

Factor the expression

More Steps

- x (2 x + 7) = 0

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

- x = 0 2 x + 7 = 0

Solve the equation for x

x = 0 2 x + 7 = 0

Solve the equation for x

More Steps

x = 0 x = - \frac{7}{2}

Determine the test intervals using the critical values

x < - \frac{7}{2} - \frac{7}{2} < x < 0 x > 0

Choose a value form each interval

x_{1} = - 5 x_{2} = - 2 x_{3} = 1

To determine if x < - \frac{7}{2} is the solution to the inequality,test if the chosen value x = - 5 satisfies the initial inequality

More Steps

x < - \frac{7}{2} is the solution x_{2} = - 2 x_{3} = 1

To determine if - \frac{7}{2} < x < 0 is the solution to the inequality,test if the chosen value x = - 2 satisfies the initial inequality

More Steps

x < - \frac{7}{2} is the solution - \frac{7}{2} < x < 0 is not a 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{7}{2} is the solution - \frac{7}{2} < x < 0 is not a solution x > 0 is the solution

Solution

x \in (- \infty, - \frac{7}{2}) \cup (0, + \infty)

Show Solution