Question
Solve the inequality
Solve the inequality by testing the values in the interval
Solve the inequality by separating into cases
c∈(−1,0)∪(1,+∞)
Evaluate
c3>c×1
Any expression multiplied by 1 remains the same
c3>c
Move the expression to the left side
c3−c>0
Rewrite the expression
c3−c=0
Factor the expression
c(c2−1)=0
Separate the equation into 2 possible cases
c=0c2−1=0
Solve the equation
More Steps

Evaluate
c2−1=0
Move the constant to the right-hand side and change its sign
c2=0+1
Removing 0 doesn't change the value,so remove it from the expression
c2=1
Take the root of both sides of the equation and remember to use both positive and negative roots
c=±1
Simplify the expression
c=±1
Separate the equation into 2 possible cases
c=1c=−1
c=0c=1c=−1
Determine the test intervals using the critical values
c<−1−1<c<00<c<1c>1
Choose a value form each interval
c1=−2c2=−21c3=21c4=2
To determine if c<−1 is the solution to the inequality,test if the chosen value c=−2 satisfies the initial inequality
More Steps

Evaluate
(−2)3>−2
Calculate
−23>−2
Calculate
−8>−2
Check the inequality
false
c<−1 is not a solutionc2=−21c3=21c4=2
To determine if −1<c<0 is the solution to the inequality,test if the chosen value c=−21 satisfies the initial inequality
More Steps

Evaluate
(−21)3>−21
Calculate
−(21)3>−21
Calculate
−0.125>−21
Calculate
−0.125>−0.5
Check the inequality
true
c<−1 is not a solution−1<c<0 is the solutionc3=21c4=2
To determine if 0<c<1 is the solution to the inequality,test if the chosen value c=21 satisfies the initial inequality
More Steps

Evaluate
(21)3>21
Calculate
231>21
Calculate
0.125>21
Calculate
0.125>0.5
Check the inequality
false
c<−1 is not a solution−1<c<0 is the solution0<c<1 is not a solutionc4=2
To determine if c>1 is the solution to the inequality,test if the chosen value c=2 satisfies the initial inequality
More Steps

Evaluate
23>2
Calculate
8>2
Check the inequality
true
c<−1 is not a solution−1<c<0 is the solution0<c<1 is not a solutionc>1 is the solution
Solution
c∈(−1,0)∪(1,+∞)
Show Solution
