Question
Solve the inequality
Solve the inequality by testing the values in the interval
Solve the inequality by separating into cases
Solve for a
a∈(−∞,−1)∪(1,+∞)
Evaluate
a2>1
Move the expression to the left side
a2−1>0
Rewrite the expression
a2−1=0
Move the constant to the right-hand side and change its sign
a2=0+1
Removing 0 doesn't change the value,so remove it from the expression
a2=1
Take the root of both sides of the equation and remember to use both positive and negative roots
a=±1
Simplify the expression
a=±1
Separate the equation into 2 possible cases
a=1a=−1
Determine the test intervals using the critical values
a<−1−1<a<1a>1
Choose a value form each interval
a1=−2a2=0a3=2
To determine if a<−1 is the solution to the inequality,test if the chosen value a=−2 satisfies the initial inequality
More Steps

Evaluate
(−2)2>1
Calculate
22>1
Calculate
4>1
Check the inequality
true
a<−1 is the solutiona2=0a3=2
To determine if −1<a<1 is the solution to the inequality,test if the chosen value a=0 satisfies the initial inequality
More Steps

Evaluate
02>1
Calculate
0>1
Check the inequality
false
a<−1 is the solution−1<a<1 is not a solutiona3=2
To determine if a>1 is the solution to the inequality,test if the chosen value a=2 satisfies the initial inequality
More Steps

Evaluate
22>1
Calculate
4>1
Check the inequality
true
a<−1 is the solution−1<a<1 is not a solutiona>1 is the solution
Solution
a∈(−∞,−1)∪(1,+∞)
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