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
a∈(−∞,0)∪(9,+∞)
Evaluate
a2−9a>0
Rewrite the expression
a2−9a=0
Factor the expression
More Steps
Evaluate
a2−9a
Rewrite the expression
a×a−a×9
Factor out a from the expression
a(a−9)
a(a−9)=0
When the product of factors equals 0,at least one factor is 0
a=0a−9=0
Solve the equation for a
More Steps
Evaluate
a−9=0
Move the constant to the right-hand side and change its sign
a=0+9
Removing 0 doesn't change the value,so remove it from the expression
a=9
a=0a=9
Determine the test intervals using the critical values
a<00<a<9a>9
Choose a value form each interval
a1=−1a2=5a3=10
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)2−9(−1)>0
Simplify
More Steps
Evaluate
(−1)2−9(−1)
Evaluate the power
1−9(−1)
Simplify
1−(−9)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
1+9
Add the numbers
10
10>0
Check the inequality
true
a<0 is the solutiona2=5a3=10
To determine if 0<a<9 is the solution to the inequality,test if the chosen value a=5 satisfies the initial inequality
More Steps
Evaluate
52−9×5>0
Simplify
More Steps
Evaluate
52−9×5
Multiply the numbers
52−45
Evaluate the power
25−45
Subtract the numbers
−20
−20>0
Check the inequality
false
a<0 is the solution0<a<9 is not a solutiona3=10
To determine if a>9 is the solution to the inequality,test if the chosen value a=10 satisfies the initial inequality
More Steps
Evaluate
102−9×10>0
Simplify
More Steps
Evaluate
102−9×10
Multiply the numbers
102−90
Evaluate the power
100−90
Subtract the numbers
10
10>0
Check the inequality
true
a<0 is the solution0<a<9 is not a solutiona>9 is the solution
Solution
a∈(−∞,0)∪(9,+∞)
Show Solution
