Solve 22q 73 > 52q^63

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve the inequality by separating into cases

0 < q < \frac{5 803 \times 7 8 ^{4}}{78}

Alternative Form

q \in (0, \frac{5 803 \times 7 8 ^{4}}{78})

Evaluate

22 q \times 73 > 52 q^{6} \times 3

Multiply the terms

1606 q > 52 q^{6} \times 3

Multiply the terms

1606 q > 156 q^{6}

Move the expression to the left side

1606 q - 156 q^{6} > 0

Rewrite the expression

1606 q - 156 q^{6} = 0

Factor the expression

2 q (803 - 78 q^{5}) = 0

Divide both sides

q (803 - 78 q^{5}) = 0

Separate the equation into 2 possible cases

q = 0 803 - 78 q^{5} = 0

Solve the equation

More Steps

q = 0 q = \frac{5 803 \times 7 8 ^{4}}{78}

Determine the test intervals using the critical values

q < 0 0 < q < \frac{5 803 \times 7 8 ^{4}}{78} q > \frac{5 803 \times 7 8 ^{4}}{78}

Choose a value form each interval

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

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 < 0 is not a solution q_{2} = 1 q_{3} = 3

To determine if 0 < q < \frac{5 803 \times 7 8 ^{4}}{78} is the solution to the inequality,test if the chosen value q = 1 satisfies the initial inequality

More Steps

q < 0 is not a solution 0 < q < \frac{5 803 \times 7 8 ^{4}}{78} is the solution q_{3} = 3

To determine if q > \frac{5 803 \times 7 8 ^{4}}{78} is the solution to the inequality,test if the chosen value q = 3 satisfies the initial inequality

More Steps

q < 0 is not a solution 0 < q < \frac{5 803 \times 7 8 ^{4}}{78} is the solution q > \frac{5 803 \times 7 8 ^{4}}{78} is not a solution

Solution

0 < q < \frac{5 803 \times 7 8 ^{4}}{78}

Alternative Form

q \in (0, \frac{5 803 \times 7 8 ^{4}}{78})

Show Solution