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 n
0<n<2
Alternative Form
n∈(0,2)
Evaluate
2n>n2
Move the expression to the left side
2n−n2>0
Rewrite the expression
2n−n2=0
Factor the expression
More Steps
Evaluate
2n−n2
Rewrite the expression
n×2−n×n
Factor out n from the expression
n(2−n)
n(2−n)=0
When the product of factors equals 0,at least one factor is 0
n=02−n=0
Solve the equation for n
More Steps
Evaluate
2−n=0
Move the constant to the right-hand side and change its sign
−n=0−2
Removing 0 doesn't change the value,so remove it from the expression
−n=−2
Change the signs on both sides of the equation
n=2
n=0n=2
Determine the test intervals using the critical values
n<00<n<2n>2
Choose a value form each interval
n1=−1n2=1n3=3
To determine if n<0 is the solution to the inequality,test if the chosen value n=−1 satisfies the initial inequality
More Steps
Evaluate
2(−1)>(−1)2
Simplify
−2>(−1)2
Evaluate the power
−2>1
Check the inequality
false
n<0 is not a solutionn2=1n3=3
To determine if 0<n<2 is the solution to the inequality,test if the chosen value n=1 satisfies the initial inequality
More Steps
Evaluate
2×1>12
Any expression multiplied by 1 remains the same
2>12
1 raised to any power equals to 1
2>1
Check the inequality
true
n<0 is not a solution0<n<2 is the solutionn3=3
To determine if n>2 is the solution to the inequality,test if the chosen value n=3 satisfies the initial inequality
More Steps
Evaluate
2×3>32
Multiply the numbers
6>32
Calculate
6>9
Check the inequality
false
n<0 is not a solution0<n<2 is the solutionn>2 is not a solution
Solution
0<n<2
Alternative Form
n∈(0,2)
Show Solution
