Question :
(x−2)(x+3)>0
Solve the inequality
Solve the inequality by testing the values in the interval
Solve the inequality by separating into cases
Solve for x
x∈(−∞,−3)∪(2,+∞)
Evaluate
(x−2)(x+3)>0
Rewrite the expression
(x−2)(x+3)=0
Separate the equation into 2 possible cases
x−2=0x+3=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=2x+3=0
Solve the equation
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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=2x=−3
Determine the test intervals using the critical values
x<−3−3<x<2x>2
Choose a value form each interval
x1=−4x2=−1x3=3
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
(−4−2)(−4+3)>0
Simplify
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Evaluate
(−4−2)(−4+3)
Subtract the numbers
(−6)(−4+3)
Remove the parentheses
−6(−4+3)
Add the numbers
−6(−1)
Simplify
6
6>0
Check the inequality
true
x<−3 is the solutionx2=−1x3=3
To determine if −3<x<2 is the solution to the inequality,test if the chosen value x=−1 satisfies the initial inequality
More Steps
Evaluate
(−1−2)(−1+3)>0
Simplify
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Evaluate
(−1−2)(−1+3)
Subtract the numbers
(−3)(−1+3)
Remove the parentheses
−3(−1+3)
Add the numbers
−3×2
Multiply the numbers
−6
−6>0
Check the inequality
false
x<−3 is the solution−3<x<2 is not a solutionx3=3
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+3)>0
Simplify
More Steps
Evaluate
(3−2)(3+3)
Subtract the numbers
1×(3+3)
Add the numbers
1×6
Any expression multiplied by 1 remains the same
6
6>0
Check the inequality
true
x<−3 is the solution−3<x<2 is not a solutionx>2 is the solution
Solution
x∈(−∞,−3)∪(2,+∞)
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