Solve 7q 11 > 5q^5

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{4 9625}{5}) \cup (0, \frac{4 9625}{5})

Evaluate

7 q \times 11 > 5 q^{5}

Multiply the terms

77 q > 5 q^{5}

Move the expression to the left side

77 q - 5 q^{5} > 0

Rewrite the expression

77 q - 5 q^{5} = 0

Factor the expression

q (77 - 5 q^{4}) = 0

Separate the equation into 2 possible cases

q = 0 77 - 5 q^{4} = 0

Solve the equation

More Steps

q = 0 q = \frac{4 9625}{5} q = - \frac{4 9625}{5}

Determine the test intervals using the critical values

q < - \frac{4 9625}{5} - \frac{4 9625}{5} < q < 0 0 < q < \frac{4 9625}{5} q > \frac{4 9625}{5}

Choose a value form each interval

q_{1} = - 3 q_{2} = - 1 q_{3} = 1 q_{4} = 3

To determine if q < - \frac{4 9625}{5} is the solution to the inequality,test if the chosen value q = - 3 satisfies the initial inequality

More Steps

q < - \frac{4 9625}{5} is the solution q_{2} = - 1 q_{3} = 1 q_{4} = 3

To determine if - \frac{4 9625}{5} < q < 0 is the solution to the inequality,test if the chosen value q = - 1 satisfies the initial inequality

More Steps

q < - \frac{4 9625}{5} is the solution - \frac{4 9625}{5} < q < 0 is not a solution q_{3} = 1 q_{4} = 3

To determine if 0 < q < \frac{4 9625}{5} is the solution to the inequality,test if the chosen value q = 1 satisfies the initial inequality

More Steps

q < - \frac{4 9625}{5} is the solution - \frac{4 9625}{5} < q < 0 is not a solution 0 < q < \frac{4 9625}{5} is the solution q_{4} = 3

To determine if q > \frac{4 9625}{5} is the solution to the inequality,test if the chosen value q = 3 satisfies the initial inequality

More Steps

q < - \frac{4 9625}{5} is the solution - \frac{4 9625}{5} < q < 0 is not a solution 0 < q < \frac{4 9625}{5} is the solution q > \frac{4 9625}{5} is not a solution

Solution

q \in (- \infty, - \frac{4 9625}{5}) \cup (0, \frac{4 9625}{5})

Show Solution