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
−4<x<3
Alternative Form
x∈(−4,3)
Evaluate
(x−3)(x+4)<0
Rewrite the expression
(x−3)(x+4)=0
Separate the equation into 2 possible cases
x−3=0x+4=0
Solve the equation
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+4=0
Solve the equation
More Steps
Evaluate
x+4=0
Move the constant to the right-hand side and change its sign
x=0−4
Removing 0 doesn't change the value,so remove it from the expression
x=−4
x=3x=−4
Determine the test intervals using the critical values
x<−4−4<x<3x>3
Choose a value form each interval
x1=−5x2=−1x3=4
To determine if x<−4 is the solution to the inequality,test if the chosen value x=−5 satisfies the initial inequality
More Steps
Evaluate
(−5−3)(−5+4)<0
Simplify
More Steps
Evaluate
(−5−3)(−5+4)
Subtract the numbers
(−8)(−5+4)
Remove the parentheses
−8(−5+4)
Add the numbers
−8(−1)
Simplify
8
8<0
Check the inequality
false
x<−4 is not a solutionx2=−1x3=4
To determine if −4<x<3 is the solution to the inequality,test if the chosen value x=−1 satisfies the initial inequality
More Steps
Evaluate
(−1−3)(−1+4)<0
Simplify
More Steps
Evaluate
(−1−3)(−1+4)
Subtract the numbers
(−4)(−1+4)
Remove the parentheses
−4(−1+4)
Add the numbers
−4×3
Multiply the numbers
−12
−12<0
Check the inequality
true
x<−4 is not a solution−4<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
(4−3)(4+4)<0
Simplify
More Steps
Evaluate
(4−3)(4+4)
Subtract the numbers
1×(4+4)
Add the numbers
1×8
Any expression multiplied by 1 remains the same
8
8<0
Check the inequality
false
x<−4 is not a solution−4<x<3 is the solutionx>3 is not a solution
Solution
−4<x<3
Alternative Form
x∈(−4,3)
Show Solution
