Question
Solve the inequality
x>1
Alternative Form
x∈(1,+∞)
Evaluate
0<x1<1
Find the domain
0<x1<1,x=0
Separate into two inequalities
{0<x1x1<1
Solve the inequality
More Steps

Evaluate
0<x1
Swap the sides of the inequality
x1>0
Solve the inequality
x>0
{x>0x1<1
Solve the inequality
More Steps

Evaluate
x1<1
Calculate
x1−1<0
Calculate
More Steps

Calculate
x1−1
Reduce fractions to a common denominator
x1−xx
Write all numerators above the common denominator
x1−x
x1−x<0
Separate the inequality into 2 possible cases
{1−x>0x<0{1−x<0x>0
Solve the inequality
More Steps

Evaluate
1−x>0
Move the constant to the right side
−x>0−1
Removing 0 doesn't change the value,so remove it from the expression
−x>−1
Change the signs on both sides of the inequality and flip the inequality sign
x<1
{x<1x<0{1−x<0x>0
Solve the inequality
More Steps

Evaluate
1−x<0
Move the constant to the right side
−x<0−1
Removing 0 doesn't change the value,so remove it from the expression
−x<−1
Change the signs on both sides of the inequality and flip the inequality sign
x>1
{x<1x<0{x>1x>0
Find the intersection
x<0{x>1x>0
Find the intersection
x<0x>1
Find the union
x∈(−∞,0)∪(1,+∞)
{x>0x∈(−∞,0)∪(1,+∞)
Find the intersection
x>1
Check if the solution is in the defined range
x>1,x=0
Solution
x>1
Alternative Form
x∈(1,+∞)
Show Solution
