Question
Solve the inequality
Solve the inequality by testing the values in the interval
Solve for x
x∈(−∞,−3+1)∪(3+1,+∞)
Evaluate
x2−2x−2>0
Rewrite the expression
x2−2x−2=0
Add or subtract both sides
x2−2x=2
Add the same value to both sides
x2−2x+1=2+1
Simplify the expression
(x−1)2=3
Take the root of both sides of the equation and remember to use both positive and negative roots
x−1=±3
Separate the equation into 2 possible cases
x−1=3x−1=−3
Move the constant to the right-hand side and change its sign
x=3+1x−1=−3
Move the constant to the right-hand side and change its sign
x=3+1x=−3+1
Determine the test intervals using the critical values
x<−3+1−3+1<x<3+1x>3+1
Choose a value form each interval
x1=−2x2=1x3=4
To determine if x<−3+1 is the solution to the inequality,test if the chosen value x=−2 satisfies the initial inequality
More Steps

Evaluate
(−2)2−2(−2)−2>0
Simplify
More Steps

Evaluate
(−2)2−2(−2)−2
Multiply the numbers
(−2)2+4−2
Evaluate the power
4+4−2
Calculate the sum or difference
6
6>0
Check the inequality
true
x<−3+1 is the solutionx2=1x3=4
To determine if −3+1<x<3+1 is the solution to the inequality,test if the chosen value x=1 satisfies the initial inequality
More Steps

Evaluate
12−2×1−2>0
Simplify
More Steps

Evaluate
12−2×1−2
1 raised to any power equals to 1
1−2×1−2
Any expression multiplied by 1 remains the same
1−2−2
Subtract the numbers
−3
−3>0
Check the inequality
false
x<−3+1 is the solution−3+1<x<3+1 is not a solutionx3=4
To determine if x>3+1 is the solution to the inequality,test if the chosen value x=4 satisfies the initial inequality
More Steps

Evaluate
42−2×4−2>0
Simplify
More Steps

Evaluate
42−2×4−2
Multiply the numbers
42−8−2
Evaluate the power
16−8−2
Subtract the numbers
6
6>0
Check the inequality
true
x<−3+1 is the solution−3+1<x<3+1 is not a solutionx>3+1 is the solution
Solution
x∈(−∞,−3+1)∪(3+1,+∞)
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