Algebra
Calculus
Trigonometry
Matrix
Question
Solve the inequality
Solve the inequality by testing the values in the interval
Solve the inequality by separating into cases
Solve for x
x∈(−∞,0)∪(1,+∞)
Evaluate
x−x2<0
Rewrite the expression
x−x2=0
Factor the expression
More Steps
Evaluate
x−x2
Rewrite the expression
x−x×x
Factor out x from the expression
x(1−x)
x(1−x)=0
When the product of factors equals 0,at least one factor is 0
x=01−x=0
Solve the equation for x
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Evaluate
1−x=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
Change the signs on both sides of the equation
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
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Evaluate
−1−(−1)2<0
Simplify
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Evaluate
−1−(−1)2
Evaluate the power
−1−1
Subtract the numbers
−2
−2<0
Check the inequality
true
x<0 is the 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−(21)2<0
Subtract the numbers
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Simplify
21−(21)2
Rewrite the expression
21−221
Evaluate the power
21−41
Reduce fractions to a common denominator
2×22−41
Multiply the numbers
42−41
Write all numerators above the common denominator
42−1
Subtract the numbers
41
41<0
Calculate
0.25<0
Check the inequality
false
x<0 is the solution0<x<1 is not a 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
2−22<0
Subtract the numbers
More Steps
Evaluate
2−22
Evaluate the power
2−4
Subtract the numbers
−2
−2<0
Check the inequality
true
x<0 is the solution0<x<1 is not a solutionx>1 is the solution
Solution
x∈(−∞,0)∪(1,+∞)
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