Algebra
Calculus
Trigonometry
Matrix
Question
Solve the inequality
x<−8
Alternative Form
x∈(−∞,−8)
Evaluate
(x2−64)6−x>0
Find the domain
More Steps
Evaluate
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
(x2−64)6−x>0,x≤6
Separate the inequality into 2 possible cases
{x2−64>06−x>0{x2−64<06−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,+∞)6−x>0{x2−64<06−x<0
Solve the inequality
More Steps
Evaluate
6−x>0
Since the left-hand side is always positive or 0,and the right-hand side is always 0,the statement is true for any value of x,except when 6−x=0
6−x=0
The only way a root could be 0 is when the radicand equals 0
6−x=0
Move the constant to the right-hand side and change its sign
−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 equation
x=6
Exclude the impossible values of x
x=6
{x∈(−∞,−8)∪(8,+∞)x=6{x2−64<06−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<86−x<0
Since the left-hand side is always positive or 0,and the right-hand side is always 0,the statement is false for any value of x
{x∈(−∞,−8)∪(8,+∞)x=6{−8<x<8x∈/R
Find the intersection
x∈(−∞,−8)∪(8,+∞){−8<x<8x∈/R
Find the intersection
x∈(−∞,−8)∪(8,+∞)x∈/R
Find the union
x∈(−∞,−8)∪(8,+∞)
Check if the solution is in the defined range
x∈(−∞,−8)∪(8,+∞),x≤6
Solution
x<−8
Alternative Form
x∈(−∞,−8)
Show Solution
