Question
Solve the inequality
Solve the inequality by testing the values in the interval
Solve the inequality by separating into cases
Solve for y
−1118<y<0
Alternative Form
y∈(−1118,0)
Evaluate
−11y2−2y×9>0
Multiply the terms
−11y2−18y>0
Rewrite the expression
−11y2−18y=0
Factor the expression
More Steps

Evaluate
−11y2−18y
Rewrite the expression
−y×11y−y×18
Factor out −y from the expression
−y(11y+18)
−y(11y+18)=0
When the product of factors equals 0,at least one factor is 0
−y=011y+18=0
Solve the equation for y
y=011y+18=0
Solve the equation for y
More Steps

Evaluate
11y+18=0
Move the constant to the right-hand side and change its sign
11y=0−18
Removing 0 doesn't change the value,so remove it from the expression
11y=−18
Divide both sides
1111y=11−18
Divide the numbers
y=11−18
Use b−a=−ba=−ba to rewrite the fraction
y=−1118
y=0y=−1118
Determine the test intervals using the critical values
y<−1118−1118<y<0y>0
Choose a value form each interval
y1=−3y2=−1y3=1
To determine if y<−1118 is the solution to the inequality,test if the chosen value y=−3 satisfies the initial inequality
More Steps

Evaluate
−11(−3)2−18(−3)>0
Simplify
More Steps

Evaluate
−11(−3)2−18(−3)
Multiply the terms
−99−18(−3)
Multiply the numbers
−99−(−54)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
−99+54
Add the numbers
−45
−45>0
Check the inequality
false
y<−1118 is not a solutiony2=−1y3=1
To determine if −1118<y<0 is the solution to the inequality,test if the chosen value y=−1 satisfies the initial inequality
More Steps

Evaluate
−11(−1)2−18(−1)>0
Simplify
More Steps

Evaluate
−11(−1)2−18(−1)
Evaluate the power
−11×1−18(−1)
Any expression multiplied by 1 remains the same
−11−18(−1)
Simplify
−11−(−18)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
−11+18
Add the numbers
7
7>0
Check the inequality
true
y<−1118 is not a solution−1118<y<0 is the solutiony3=1
To determine if y>0 is the solution to the inequality,test if the chosen value y=1 satisfies the initial inequality
More Steps

Evaluate
−11×12−18×1>0
Simplify
More Steps

Evaluate
−11×12−18×1
1 raised to any power equals to 1
−11×1−18×1
Any expression multiplied by 1 remains the same
−11−18×1
Any expression multiplied by 1 remains the same
−11−18
Subtract the numbers
−29
−29>0
Check the inequality
false
y<−1118 is not a solution−1118<y<0 is the solutiony>0 is not a solution
Solution
−1118<y<0
Alternative Form
y∈(−1118,0)
Show Solution
