Question
Solve the inequality
Solve the inequality by testing the values in the interval
Solve the inequality by separating into cases
Solve for x
0<x<1
Alternative Form
x∈(0,1)
Evaluate
x2−x×1<0
Any expression multiplied by 1 remains the same
x2−x<0
Rewrite the expression
x2−x=0
Factor the expression
More Steps

Evaluate
x2−x
Rewrite the expression
x×x−x
Factor out x from the expression
x(x−1)
x(x−1)=0
When the product of factors equals 0,at least one factor is 0
x=0x−1=0
Solve the equation for x
More Steps

Evaluate
x−1=0
Move the constant to the right-hand side and change its sign
x=0+1
Removing 0 doesn't change the value,so remove it from the expression
x=1
x=0x=1
Determine the test intervals using the critical values
x<00<x<1x>1
Choose a value form each interval
x1=−1x2=21x3=2
To determine if x<0 is the solution to the inequality,test if the chosen value x=−1 satisfies the initial inequality
More Steps

Evaluate
(−1)2−(−1)<0
Simplify
More Steps

Evaluate
(−1)2−(−1)
Evaluate the power
1−(−1)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
1+1
Add the numbers
2
2<0
Check the inequality
false
x<0 is not a solutionx2=21x3=2
To determine if 0<x<1 is the solution to the inequality,test if the chosen value x=21 satisfies the initial inequality
More Steps

Evaluate
(21)2−21<0
Subtract the numbers
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Simplify
(21)2−21
Rewrite the expression
221−21
Evaluate the power
41−21
Reduce fractions to a common denominator
41−2×22
Multiply the numbers
41−42
Write all numerators above the common denominator
41−2
Subtract the numbers
4−1
Use b−a=−ba=−ba to rewrite the fraction
−41
−41<0
Calculate
−0.25<0
Check the inequality
true
x<0 is not a solution0<x<1 is the solutionx3=2
To determine if x>1 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
false
x<0 is not a solution0<x<1 is the solutionx>1 is not a solution
Solution
0<x<1
Alternative Form
x∈(0,1)
Show Solution
