Algebra
Calculus
Trigonometry
Matrix
Question
Solve the inequality
a∈(−π,0)∪(π,π)
Evaluate
aπ<a<π
Find the domain
aπ<a<π,a=0
Separate into two inequalities
{aπ<aa<π
Solve the inequality
More Steps
Evaluate
aπ<a
Move the expression to the left side
aπ−a<0
Subtract the terms
More Steps
Evaluate
aπ−a
Reduce fractions to a common denominator
aπ−aa×a
Write all numerators above the common denominator
aπ−a×a
Multiply the terms
aπ−a2
aπ−a2<0
Separate the inequality into 2 possible cases
{π−a2>0a<0{π−a2<0a>0
Solve the inequality
More Steps
Evaluate
π−a2>0
Rewrite the expression
−a2>−π
Change the signs on both sides of the inequality and flip the inequality sign
a2<π
Take the 2-th root on both sides of the inequality
a2<π
Calculate
∣a∣<π
Separate the inequality into 2 possible cases
{a<πa>−π
Find the intersection
−π<a<π
{−π<a<πa<0{π−a2<0a>0
Solve the inequality
More Steps
Evaluate
π−a2<0
Rewrite the expression
−a2<−π
Change the signs on both sides of the inequality and flip the inequality sign
a2>π
Take the 2-th root on both sides of the inequality
a2>π
Calculate
∣a∣>π
Separate the inequality into 2 possible cases
a>πa<−π
Find the union
a∈(−∞,−π)∪(π,+∞)
{−π<a<πa<0{a∈(−∞,−π)∪(π,+∞)a>0
Find the intersection
−π<a<0{a∈(−∞,−π)∪(π,+∞)a>0
Find the intersection
−π<a<0a>π
Find the union
a∈(−π,0)∪(π,+∞)
{a∈(−π,0)∪(π,+∞)a<π
Find the intersection
a∈(−π,0)∪(π,π)
Check if the solution is in the defined range
a∈(−π,0)∪(π,π),a=0
Solution
a∈(−π,0)∪(π,π)
Show Solution
