Solve 3*x^2+2*x>5

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{5}{3}) \cup (1, + \infty)

Evaluate

3 x^{2} + 2 x > 5

Move the expression to the left side

3 x^{2} + 2 x - 5 > 0

Rewrite the expression

3 x^{2} + 2 x - 5 = 0

Factor the expression

More Steps

(x - 1) (3 x + 5) = 0

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

x - 1 = 0 3 x + 5 = 0

Solve the equation for x

More Steps

x = 1 3 x + 5 = 0

Solve the equation for x

More Steps

x = 1 x = - \frac{5}{3}

Determine the test intervals using the critical values

x < - \frac{5}{3} - \frac{5}{3} < x < 1 x > 1

Choose a value form each interval

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

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 < - \frac{5}{3} is the solution x_{2} = - 1 x_{3} = 2

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

More Steps

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

To determine if x > 1 is the solution to the inequality,test if the chosen value x = 2 satisfies the initial inequality

More Steps

x < - \frac{5}{3} is the solution - \frac{5}{3} < x < 1 is not a solution x > 1 is the solution

Solution

x \in (- \infty, - \frac{5}{3}) \cup (1, + \infty)

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