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<3
Alternative Form
x∈(−2,3)
Evaluate
x2−x−6<0
Rewrite the expression
x2−x−6=0
Factor the expression
More Steps
Evaluate
x2−x−6
Rewrite the expression
x2+(2−3)x−6
Calculate
x2+2x−3x−6
Rewrite the expression
x×x+x×2−3x−3×2
Factor out x from the expression
x(x+2)−3x−3×2
Factor out −3 from the expression
x(x+2)−3(x+2)
Factor out x+2 from the expression
(x−3)(x+2)
(x−3)(x+2)=0
When the product of factors equals 0,at least one factor is 0
x−3=0x+2=0
Solve the equation for x
More Steps
Evaluate
x−3=0
Move the constant to the right-hand side and change its sign
x=0+3
Removing 0 doesn't change the value,so remove it from the expression
x=3
x=3x+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=3x=−2
Determine the test intervals using the critical values
x<−2−2<x<3x>3
Choose a value form each interval
x1=−3x2=1x3=4
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−(−3)−6<0
Subtract the numbers
More Steps
Evaluate
(−3)2−(−3)−6
Evaluate the power
9−(−3)−6
Subtract the terms
12−6
Subtract the numbers
6
6<0
Check the inequality
false
x<−2 is not a solutionx2=1x3=4
To determine if −2<x<3 is the solution to the inequality,test if the chosen value x=1 satisfies the initial inequality
More Steps
Evaluate
12−1−6<0
Simplify
More Steps
Evaluate
12−1−6
1 raised to any power equals to 1
1−1−6
Apply the inverse property of addition
−6
−6<0
Check the inequality
true
x<−2 is not a solution−2<x<3 is the solutionx3=4
To determine if x>3 is the solution to the inequality,test if the chosen value x=4 satisfies the initial inequality
More Steps
Evaluate
42−4−6<0
Subtract the numbers
More Steps
Evaluate
42−4−6
Evaluate the power
16−4−6
Subtract the numbers
6
6<0
Check the inequality
false
x<−2 is not a solution−2<x<3 is the solutionx>3 is not a solution
Solution
−2<x<3
Alternative Form
x∈(−2,3)
Show Solution
