Algebra
Calculus
Trigonometry
Matrix
Question
Solve the inequality
x∈(−∞,−8)∪(6,8)
Evaluate
(x2−64)36−x>0
Separate the inequality into 2 possible cases
{x2−64>036−x>0{x2−64<036−x<0
Solve the inequality
More Steps
Evaluate
x2−64>0
Move the constant to the right side
x2>64
Take the 2-th root on both sides of the inequality
x2>64
Calculate
∣x∣>8
Separate the inequality into 2 possible cases
x>8x<−8
Find the union
x∈(−∞,−8)∪(8,+∞)
{x∈(−∞,−8)∪(8,+∞)36−x>0{x2−64<036−x<0
Solve the inequality
More Steps
Evaluate
36−x>0
Raise both sides of the inequality to the power of 3
6−x>0
Move the constant to the right side
−x>0−6
Removing 0 doesn't change the value,so remove it from the expression
−x>−6
Change the signs on both sides of the inequality and flip the inequality sign
x<6
{x∈(−∞,−8)∪(8,+∞)x<6{x2−64<036−x<0
Solve the inequality
More Steps
Evaluate
x2−64<0
Move the constant to the right side
x2<64
Take the 2-th root on both sides of the inequality
x2<64
Calculate
∣x∣<8
Separate the inequality into 2 possible cases
{x<8x>−8
Find the intersection
−8<x<8
{x∈(−∞,−8)∪(8,+∞)x<6{−8<x<836−x<0
Solve the inequality
More Steps
Evaluate
36−x<0
Raise both sides of the inequality to the power of 3
6−x<0
Move the constant to the right side
−x<0−6
Removing 0 doesn't change the value,so remove it from the expression
−x<−6
Change the signs on both sides of the inequality and flip the inequality sign
x>6
{x∈(−∞,−8)∪(8,+∞)x<6{−8<x<8x>6
Find the intersection
x<−8{−8<x<8x>6
Find the intersection
x<−86<x<8
Solution
x∈(−∞,−8)∪(6,8)
Show Solution
