Question
Solve the inequality
Solve the inequality by testing the values in the interval
Solve the inequality by separating into cases
0<q<785803×784
Alternative Form
q∈(0,785803×784)
Evaluate
22q×73>52q6×3
Multiply the terms
1606q>52q6×3
Multiply the terms
1606q>156q6
Move the expression to the left side
1606q−156q6>0
Rewrite the expression
1606q−156q6=0
Factor the expression
2q(803−78q5)=0
Divide both sides
q(803−78q5)=0
Separate the equation into 2 possible cases
q=0803−78q5=0
Solve the equation
More Steps

Evaluate
803−78q5=0
Move the constant to the right-hand side and change its sign
−78q5=0−803
Removing 0 doesn't change the value,so remove it from the expression
−78q5=−803
Change the signs on both sides of the equation
78q5=803
Divide both sides
7878q5=78803
Divide the numbers
q5=78803
Take the 5-th root on both sides of the equation
5q5=578803
Calculate
q=578803
Simplify the root
More Steps

Evaluate
578803
To take a root of a fraction,take the root of the numerator and denominator separately
5785803
Multiply by the Conjugate
578×57845803×5784
The product of roots with the same index is equal to the root of the product
578×57845803×784
Multiply the numbers
785803×784
q=785803×784
q=0q=785803×784
Determine the test intervals using the critical values
q<00<q<785803×784q>785803×784
Choose a value form each interval
q1=−1q2=1q3=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

Evaluate
1606(−1)>156(−1)6
Simplify
−1606>156(−1)6
Simplify
More Steps

Evaluate
156(−1)6
Evaluate the power
156×1
Any expression multiplied by 1 remains the same
156
−1606>156
Check the inequality
false
q<0 is not a solutionq2=1q3=3
To determine if 0<q<785803×784 is the solution to the inequality,test if the chosen value q=1 satisfies the initial inequality
More Steps

Evaluate
1606×1>156×16
Any expression multiplied by 1 remains the same
1606>156×16
Simplify
More Steps

Evaluate
156×16
1 raised to any power equals to 1
156×1
Any expression multiplied by 1 remains the same
156
1606>156
Check the inequality
true
q<0 is not a solution0<q<785803×784 is the solutionq3=3
To determine if q>785803×784 is the solution to the inequality,test if the chosen value q=3 satisfies the initial inequality
More Steps

Evaluate
1606×3>156×36
Multiply the numbers
4818>156×36
Multiply the terms
More Steps

Evaluate
156×36
Evaluate the power
156×729
Multiply the numbers
113724
4818>113724
Check the inequality
false
q<0 is not a solution0<q<785803×784 is the solutionq>785803×784 is not a solution
Solution
0<q<785803×784
Alternative Form
q∈(0,785803×784)
Show Solution
