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 a
0<a<1
Alternative Form
a∈(0,1)
Evaluate
a2<a
Move the expression to the left side
a2−a<0
Rewrite the expression
a2−a=0
Factor the expression
More Steps
Evaluate
a2−a
Rewrite the expression
a×a−a
Factor out a from the expression
a(a−1)
a(a−1)=0
When the product of factors equals 0,at least one factor is 0
a=0a−1=0
Solve the equation for a
More Steps
Evaluate
a−1=0
Move the constant to the right-hand side and change its sign
a=0+1
Removing 0 doesn't change the value,so remove it from the expression
a=1
a=0a=1
Determine the test intervals using the critical values
a<00<a<1a>1
Choose a value form each interval
a1=−1a2=21a3=2
To determine if a<0 is the solution to the inequality,test if the chosen value a=−1 satisfies the initial inequality
More Steps
Evaluate
(−1)2<−1
Evaluate the power
1<−1
Check the inequality
false
a<0 is not a solutiona2=21a3=2
To determine if 0<a<1 is the solution to the inequality,test if the chosen value a=21 satisfies the initial inequality
More Steps
Evaluate
(21)2<21
Calculate
221<21
Calculate
0.25<21
Calculate
0.25<0.5
Check the inequality
true
a<0 is not a solution0<a<1 is the solutiona3=2
To determine if a>1 is the solution to the inequality,test if the chosen value a=2 satisfies the initial inequality
More Steps
Evaluate
22<2
Calculate
4<2
Check the inequality
false
a<0 is not a solution0<a<1 is the solutiona>1 is not a solution
Solution
0<a<1
Alternative Form
a∈(0,1)
Show Solution
