Algebra
Calculus
Trigonometry
Matrix
Question
Solve the inequality
x∈(−1,0)∪(1,34)
Evaluate
x:1<x3<4
Separate into two inequalities
{x÷1<x3x3<4
Solve the inequality
More Steps
Evaluate
x÷1<x3
Divide the terms
More Steps
Evaluate
x÷1
Rewrite the expression
1x
Divide the terms
x
x<x3
Move the expression to the left side
x−x3<0
Factor the expression
x(1−x2)<0
Separate the inequality into 2 possible cases
{x>01−x2<0{x<01−x2>0
Solve the inequality
More Steps
Evaluate
1−x2<0
Rewrite the expression
−x2<−1
Change the signs on both sides of the inequality and flip the inequality sign
x2>1
Take the 2-th root on both sides of the inequality
x2>1
Calculate
∣x∣>1
Separate the inequality into 2 possible cases
x>1x<−1
Find the union
x∈(−∞,−1)∪(1,+∞)
{x>0x∈(−∞,−1)∪(1,+∞){x<01−x2>0
Solve the inequality
More Steps
Evaluate
1−x2>0
Rewrite the expression
−x2>−1
Change the signs on both sides of the inequality and flip the inequality sign
x2<1
Take the 2-th root on both sides of the inequality
x2<1
Calculate
∣x∣<1
Separate the inequality into 2 possible cases
{x<1x>−1
Find the intersection
−1<x<1
{x>0x∈(−∞,−1)∪(1,+∞){x<0−1<x<1
Find the intersection
x>1{x<0−1<x<1
Find the intersection
x>1−1<x<0
Find the union
x∈(−1,0)∪(1,+∞)
{x∈(−1,0)∪(1,+∞)x3<4
Solve the inequality
More Steps
Evaluate
x3<4
Take the 3-th root on both sides of the equation
3x3<34
Calculate
x<34
{x∈(−1,0)∪(1,+∞)x<34
Solution
x∈(−1,0)∪(1,34)
Show Solution
