Solve 50q^43>-11q 70

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve the inequality by separating into cases

q \in (- \infty, - \frac{3 17325}{15}) \cup (0, + \infty)

Evaluate

50 q^{4} \times 3 > - 11 q \times 70

Multiply the terms

150 q^{4} > - 11 q \times 70

Multiply the terms

150 q^{4} > - 770 q

Move the expression to the left side

150 q^{4} - (- 770 q) > 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

150 q^{4} + 770 q > 0

Rewrite the expression

150 q^{4} + 770 q = 0

Factor the expression

10 q (15 q^{3} + 77) = 0

Divide both sides

q (15 q^{3} + 77) = 0

Separate the equation into 2 possible cases

q = 0 15 q^{3} + 77 = 0

Solve the equation

More Steps

q = 0 q = - \frac{3 17325}{15}

Determine the test intervals using the critical values

q < - \frac{3 17325}{15} - \frac{3 17325}{15} < q < 0 q > 0

Choose a value form each interval

q_{1} = - 3 q_{2} = - 1 q_{3} = 1

To determine if q < - \frac{3 17325}{15} is the solution to the inequality,test if the chosen value q = - 3 satisfies the initial inequality

More Steps

q < - \frac{3 17325}{15} is the solution q_{2} = - 1 q_{3} = 1

To determine if - \frac{3 17325}{15} < q < 0 is the solution to the inequality,test if the chosen value q = - 1 satisfies the initial inequality

More Steps

q < - \frac{3 17325}{15} is the solution - \frac{3 17325}{15} < q < 0 is not a solution q_{3} = 1

To determine if q > 0 is the solution to the inequality,test if the chosen value q = 1 satisfies the initial inequality

More Steps

q < - \frac{3 17325}{15} is the solution - \frac{3 17325}{15} < q < 0 is not a solution q > 0 is the solution

Solution

q \in (- \infty, - \frac{3 17325}{15}) \cup (0, + \infty)

Show Solution