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<1
Alternative Form
x∈(−∞,1)
Evaluate
x2×x−1<0
Multiply the terms
More Steps

Evaluate
x2×x
Use the product rule an×am=an+m to simplify the expression
x2+1
Add the numbers
x3
x3−1<0
Rewrite the expression
x3−1=0
Move the constant to the right-hand side and change its sign
x3=0+1
Removing 0 doesn't change the value,so remove it from the expression
x3=1
Take the 3-th root on both sides of the equation
3x3=31
Calculate
x=31
Simplify the root
x=1
Determine the test intervals using the critical values
x<1x>1
Choose a value form each interval
x1=0x2=2
To determine if x<1 is the solution to the inequality,test if the chosen value x=0 satisfies the initial inequality
More Steps

Evaluate
03−1<0
Simplify
More Steps

Evaluate
03−1
Calculate
0−1
Removing 0 doesn't change the value,so remove it from the expression
−1
−1<0
Check the inequality
true
x<1 is the solutionx2=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
23−1<0
Subtract the numbers
More Steps

Evaluate
23−1
Evaluate the power
8−1
Subtract the numbers
7
7<0
Check the inequality
false
x<1 is the solutionx>1 is not a solution
Solution
x<1
Alternative Form
x∈(−∞,1)
Show Solution
