Question
Solve the inequality
Solve the inequality by testing the values in the interval
Solve the inequality by separating into cases
Solve for r
r∈(−∞,0)∪(1,+∞)
Evaluate
r×1<r2
Any expression multiplied by 1 remains the same
r<r2
Move the expression to the left side
r−r2<0
Rewrite the expression
r−r2=0
Factor the expression
More Steps

Evaluate
r−r2
Rewrite the expression
r−r×r
Factor out r from the expression
r(1−r)
r(1−r)=0
When the product of factors equals 0,at least one factor is 0
r=01−r=0
Solve the equation for r
More Steps

Evaluate
1−r=0
Move the constant to the right-hand side and change its sign
−r=0−1
Removing 0 doesn't change the value,so remove it from the expression
−r=−1
Change the signs on both sides of the equation
r=1
r=0r=1
Determine the test intervals using the critical values
r<00<r<1r>1
Choose a value form each interval
r1=−1r2=21r3=2
To determine if r<0 is the solution to the inequality,test if the chosen value r=−1 satisfies the initial inequality
More Steps

Evaluate
−1<(−1)2
Evaluate the power
−1<1
Check the inequality
true
r<0 is the solutionr2=21r3=2
To determine if 0<r<1 is the solution to the inequality,test if the chosen value r=21 satisfies the initial inequality
More Steps

Evaluate
21<(21)2
Rewrite the expression
21<221
Cross multiply
22<2
Calculate
4<2
Check the inequality
false
r<0 is the solution0<r<1 is not a solutionr3=2
To determine if r>1 is the solution to the inequality,test if the chosen value r=2 satisfies the initial inequality
More Steps

Evaluate
2<22
Calculate
2<4
Check the inequality
true
r<0 is the solution0<r<1 is not a solutionr>1 is the solution
Solution
r∈(−∞,0)∪(1,+∞)
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