Algebra
Calculus
Trigonometry
Matrix
Question
Solve the inequality
Solve the inequality by separating into cases
Solve for x
x∈(−2,0)∪(0,2)
Evaluate
xx3−2<2
Find the domain
xx3−2<2,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<2
Move the expression to the left side
x2−2−2<0
Subtract the numbers
x2−4<0
Use a2−b2=(a−b)(a+b) to factor the expression
(x−2)(x+2)<0
Separate the inequality into 2 possible cases
{x−2>0x+2<0{x−2<0x+2>0
Solve the inequality
More Steps
Evaluate
x−2>0
Move the constant to the right side
x>0+2
Removing 0 doesn't change the value,so remove it from the expression
x>2
{x>2x+2<0{x−2<0x+2>0
Solve the inequality
More Steps
Evaluate
x+2<0
Move the constant to the right side
x<0−2
Removing 0 doesn't change the value,so remove it from the expression
x<−2
{x>2x<−2{x−2<0x+2>0
Solve the inequality
More Steps
Evaluate
x−2<0
Move the constant to the right side
x<0+2
Removing 0 doesn't change the value,so remove it from the expression
x<2
{x>2x<−2{x<2x+2>0
Solve the inequality
More Steps
Evaluate
x+2>0
Move the constant to the right side
x>0−2
Removing 0 doesn't change the value,so remove it from the expression
x>−2
{x>2x<−2{x<2x>−2
Find the intersection
x∈∅{x<2x>−2
Find the intersection
x∈∅−2<x<2
Find the union
−2<x<2
Check if the solution is in the defined range
−2<x<2,x=0
Solution
x∈(−2,0)∪(0,2)
Show Solution
