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<−1
Alternative Form
x∈(−∞,−1)
Evaluate
x3−x2×2x−1>0
Simplify
More Steps
Evaluate
x3−x2×2x−1
Multiply
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Multiply the terms
−x2×2x
Multiply the terms with the same base by adding their exponents
−x2+1×2
Add the numbers
−x3×2
Use the commutative property to reorder the terms
−2x3
x3−2x3−1
Subtract the terms
More Steps
Evaluate
x3−2x3
Collect like terms by calculating the sum or difference of their coefficients
(1−2)x3
Subtract the numbers
−x3
−x3−1
−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
Change the signs on both sides of the equation
x3=−1
Take the 3-th root on both sides of the equation
3x3=3−1
Calculate
x=3−1
Simplify the root
More Steps
Evaluate
3−1
An odd root of a negative radicand is always a negative
−31
Simplify the radical expression
−1
x=−1
Determine the test intervals using the critical values
x<−1x>−1
Choose a value form each interval
x1=−2x2=0
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)3−1>0
Subtract the numbers
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Evaluate
−(−2)3−1
Simplify
23−1
Evaluate the power
8−1
Subtract the numbers
7
7>0
Check the inequality
true
x<−1 is the solutionx2=0
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
Simplify
0−1
Removing 0 doesn't change the value,so remove it from the expression
−1
−1>0
Check the inequality
false
x<−1 is the solutionx>−1 is not a solution
Solution
x<−1
Alternative Form
x∈(−∞,−1)
Show Solution
