Question
Solve the inequality
Solve the inequality by testing the values in the interval
Solve for r
r<−36
Alternative Form
r∈(−∞,−36)
Evaluate
r3<−6
Move the expression to the left side
r3−(−6)<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
r3+6<0
Rewrite the expression
r3+6=0
Move the constant to the right-hand side and change its sign
r3=0−6
Removing 0 doesn't change the value,so remove it from the expression
r3=−6
Take the 3-th root on both sides of the equation
3r3=3−6
Calculate
r=3−6
An odd root of a negative radicand is always a negative
r=−36
Determine the test intervals using the critical values
r<−36r>−36
Choose a value form each interval
r1=−3r2=−1
To determine if r<−36 is the solution to the inequality,test if the chosen value r=−3 satisfies the initial inequality
More Steps
Evaluate
(−3)3<−6
Calculate
−33<−6
Calculate
−27<−6
Check the inequality
true
r<−36 is the solutionr2=−1
To determine if r>−36 is the solution to the inequality,test if the chosen value r=−1 satisfies the initial inequality
More Steps
Evaluate
(−1)3<−6
Calculate
−1<−6
Check the inequality
false
r<−36 is the solutionr>−36 is not a solution
Solution
r<−36
Alternative Form
r∈(−∞,−36)
Show Solution