Algebra
Calculus
Trigonometry
Matrix
Question
Solve the inequality
Solve the inequality by testing the values in the interval
Solve for x
x∈(−∞,−2)∪(2,+∞)
Evaluate
xx3−2>0
Find the domain
xx3−2>0,x=0
Divide the terms
More Steps
Evaluate
xx3
Use the product rule aman=an−m to simplify the expression
1x3−1
Simplify
x3−1
Divide the terms
x2
x2−2>0
Rewrite the expression
x2−2=0
Move the constant to the right-hand side and change its sign
x2=0+2
Removing 0 doesn't change the value,so remove it from the expression
x2=2
Take the root of both sides of the equation and remember to use both positive and negative roots
x=±2
Separate the equation into 2 possible cases
x=2x=−2
Determine the test intervals using the critical values
x<−2−2<x<2x>2
Choose a value form each interval
x1=−2x2=0x3=2
To determine if x<−2 is the solution to the inequality,test if the chosen value x=−2 satisfies the initial inequality
More Steps
Evaluate
(−2)2−2>0
Subtract the numbers
More Steps
Evaluate
(−2)2−2
Simplify
22−2
Evaluate the power
4−2
Subtract the numbers
2
2>0
Check the inequality
true
x<−2 is the solutionx2=0x3=2
To determine if −2<x<2 is the solution to the inequality,test if the chosen value x=0 satisfies the initial inequality
More Steps
Evaluate
02−2>0
Simplify
More Steps
Evaluate
02−2
Calculate
0−2
Removing 0 doesn't change the value,so remove it from the expression
−2
−2>0
Check the inequality
false
x<−2 is the solution−2<x<2 is not a solutionx3=2
To determine if x>2 is the solution to the inequality,test if the chosen value x=2 satisfies the initial inequality
More Steps
Evaluate
22−2>0
Subtract the numbers
More Steps
Evaluate
22−2
Evaluate the power
4−2
Subtract the numbers
2
2>0
Check the inequality
true
x<−2 is the solution−2<x<2 is not a solutionx>2 is the solution
The original inequality is a strict inequality,so does not include the critical value ,the final solution is x∈(−∞,−2)∪(2,+∞)
x∈(−∞,−2)∪(2,+∞)
Check if the solution is in the defined range
x∈(−∞,−2)∪(2,+∞),x=0
Solution
x∈(−∞,−2)∪(2,+∞)
Show Solution
