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 x
−2<x<8
Alternative Form
x∈(−2,8)
Evaluate
x2−6x−16<0
Rewrite the expression
x2−6x−16=0
Factor the expression
More Steps
Evaluate
x2−6x−16
Rewrite the expression
x2+(2−8)x−16
Calculate
x2+2x−8x−16
Rewrite the expression
x×x+x×2−8x−8×2
Factor out x from the expression
x(x+2)−8x−8×2
Factor out −8 from the expression
x(x+2)−8(x+2)
Factor out x+2 from the expression
(x−8)(x+2)
(x−8)(x+2)=0
When the product of factors equals 0,at least one factor is 0
x−8=0x+2=0
Solve the equation for x
More Steps
Evaluate
x−8=0
Move the constant to the right-hand side and change its sign
x=0+8
Removing 0 doesn't change the value,so remove it from the expression
x=8
x=8x+2=0
Solve the equation for x
More Steps
Evaluate
x+2=0
Move the constant to the right-hand side and change its sign
x=0−2
Removing 0 doesn't change the value,so remove it from the expression
x=−2
x=8x=−2
Determine the test intervals using the critical values
x<−2−2<x<8x>8
Choose a value form each interval
x1=−3x2=3x3=9
To determine if x<−2 is the solution to the inequality,test if the chosen value x=−3 satisfies the initial inequality
More Steps
Evaluate
(−3)2−6(−3)−16<0
Simplify
More Steps
Evaluate
(−3)2−6(−3)−16
Multiply the numbers
(−3)2+18−16
Evaluate the power
9+18−16
Calculate the sum or difference
11
11<0
Check the inequality
false
x<−2 is not a solutionx2=3x3=9
To determine if −2<x<8 is the solution to the inequality,test if the chosen value x=3 satisfies the initial inequality
More Steps
Evaluate
32−6×3−16<0
Simplify
More Steps
Evaluate
32−6×3−16
Multiply the numbers
32−18−16
Evaluate the power
9−18−16
Subtract the numbers
−25
−25<0
Check the inequality
true
x<−2 is not a solution−2<x<8 is the solutionx3=9
To determine if x>8 is the solution to the inequality,test if the chosen value x=9 satisfies the initial inequality
More Steps
Evaluate
92−6×9−16<0
Simplify
More Steps
Evaluate
92−6×9−16
Multiply the numbers
92−54−16
Evaluate the power
81−54−16
Subtract the numbers
11
11<0
Check the inequality
false
x<−2 is not a solution−2<x<8 is the solutionx>8 is not a solution
Solution
−2<x<8
Alternative Form
x∈(−2,8)
Show Solution
