Algebra
Calculus
Trigonometry
Matrix
Question
Solve the inequality
2<x≤6
Alternative Form
x∈(2,6]
Evaluate
6−x<x
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
6−x<x,x≤6
Separate the inequality into 2 possible cases
6−x<x,x≥06−x<x,x<0
Solve the inequality
More Steps
Solve the inequality
6−x<x
Square both sides of the inequality
6−x<x2
Move the expression to the left side
6−x−x2<0
Move the constant to the right side
−x−x2<0−6
Add the terms
−x−x2<−6
Evaluate
x2+x>6
Add the same value to both sides
x2+x+41>6+41
Evaluate
x2+x+41>425
Evaluate
(x+21)2>425
Take the 2-th root on both sides of the inequality
(x+21)2>425
Calculate
x+21>25
Separate the inequality into 2 possible cases
x+21>25x+21<−25
Calculate
More Steps
Evaluate
x+21>25
Move the constant to the right side
x>25−21
Subtract the numbers
x>2
x>2x+21<−25
Calculate
More Steps
Evaluate
x+21<−25
Move the constant to the right side
x<−25−21
Subtract the numbers
x<−3
x>2x<−3
Find the union
x∈(−∞,−3)∪(2,+∞)
x∈(−∞,−3)∪(2,+∞),x≥06−x<x,x<0
Since the left-hand side is always positive or 0,and the right-hand side is always negative,the statement is false for any value of x
x∈(−∞,−3)∪(2,+∞),x≥0x∈∅,x<0
Find the intersection
x>2x∈∅,x<0
Find the intersection
x>2x∈∅
Find the union
x>2
Check if the solution is in the defined range
x>2,x≤6
Solution
2<x≤6
Alternative Form
x∈(2,6]
Show Solution
