Question
Solve the inequality
Solve the inequality by testing the values in the interval
Solve for x
x≥36
Alternative Form
x∈[36,+∞)
Evaluate
x2×x−6≥0
Multiply the terms
More Steps

Evaluate
x2×x
Use the product rule an×am=an+m to simplify the expression
x2+1
Add the numbers
x3
x3−6≥0
Rewrite the expression
x3−6=0
Move the constant to the right-hand side and change its sign
x3=0+6
Removing 0 doesn't change the value,so remove it from the expression
x3=6
Take the 3-th root on both sides of the equation
3x3=36
Calculate
x=36
Determine the test intervals using the critical values
x<36x>36
Choose a value form each interval
x1=1x2=3
To determine if x<36 is the solution to the inequality,test if the chosen value x=1 satisfies the initial inequality
More Steps

Evaluate
13−6≥0
Simplify
More Steps

Evaluate
13−6
1 raised to any power equals to 1
1−6
Subtract the numbers
−5
−5≥0
Check the inequality
false
x<36 is not a solutionx2=3
To determine if x>36 is the solution to the inequality,test if the chosen value x=3 satisfies the initial inequality
More Steps

Evaluate
33−6≥0
Subtract the numbers
More Steps

Evaluate
33−6
Evaluate the power
27−6
Subtract the numbers
21
21≥0
Check the inequality
true
x<36 is not a solutionx>36 is the solution
The original inequality is a nonstrict inequality,so include the critical value in the solution
x≥36 is the solution
Solution
x≥36
Alternative Form
x∈[36,+∞)
Show Solution
