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
x∈(−∞,−2)∪(3,+∞)
Evaluate
(x−3)(x+2)>0
Rewrite the expression
(x−3)(x+2)=0
Separate the equation into 2 possible cases
x−3=0x+2=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+2=0
Solve the equation
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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
(−3−3)(−3+2)>0
Simplify
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Evaluate
(−3−3)(−3+2)
Subtract the numbers
(−6)(−3+2)
Remove the parentheses
−6(−3+2)
Add the numbers
−6(−1)
Simplify
6
6>0
Check the inequality
true
x<−2 is the 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
(1−3)(1+2)>0
Simplify
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Evaluate
(1−3)(1+2)
Subtract the numbers
(−2)(1+2)
Remove the parentheses
−2(1+2)
Add the numbers
−2×3
Multiply the numbers
−6
−6>0
Check the inequality
false
x<−2 is the solution−2<x<3 is not a 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+2)>0
Simplify
More Steps
Evaluate
(4−3)(4+2)
Subtract the numbers
1×(4+2)
Add the numbers
1×6
Any expression multiplied by 1 remains the same
6
6>0
Check the inequality
true
x<−2 is the solution−2<x<3 is not a solutionx>3 is the solution
Solution
x∈(−∞,−2)∪(3,+∞)
Show Solution
