Algebra
Calculus
Trigonometry
Matrix
Question
Solve the inequality
x∈∅
Alternative Form
No solution
Evaluate
x−2−x>2
Find the domain
More Steps
Evaluate
{x≥02−x≥0
Calculate
More Steps
Evaluate
2−x≥0
Move the constant to the right side
−x≥0−2
Removing 0 doesn't change the value,so remove it from the expression
−x≥−2
Change the signs on both sides of the inequality and flip the inequality sign
x≤2
{x≥0x≤2
Find the intersection
0≤x≤2
x−2−x>2,0≤x≤2
Move the expression to the left side
x−2−x−2>0
Move the expression to the right side
x>2−x+2
Raise both sides of the inequality to the power of 2
x>(2−x+2)2
Expand the expression
x>4−x+24−2x
Move the expression to the left side
x−(4−x+24−2x)>0
Subtract the terms
More Steps
Evaluate
x−(4−x+24−2x)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
x−4+x−24−2x
Add the terms
More Steps
Evaluate
x+x
Collect like terms by calculating the sum or difference of their coefficients
(1+1)x
Add the numbers
2x
2x−4−24−2x
2x−4−24−2x>0
Move the expression to the right side
−24−2x>−2x+4
Divide both sides
4−2x<x−2
Separate the inequality into 2 possible cases
4−2x<x−2,x−2≥04−2x<x−2,x−2<0
Solve the inequality
More Steps
Solve the inequality
4−2x<x−2
Square both sides of the inequality
4−2x<(x−2)2
Move the expression to the left side
4−2x−(x−2)2<0
Calculate
More Steps
Evaluate
4−2x−(x−2)2
Expand the expression
4−2x−x2+4x−4
Since two opposites add up to 0,remove them form the expression
−2x−x2+4x
Add the terms
2x−x2
2x−x2<0
Evaluate
x2−2x>0
Add the same value to both sides
x2−2x+1>1
Evaluate
(x−1)2>1
Take the 2-th root on both sides of the inequality
(x−1)2>1
Calculate
∣x−1∣>1
Separate the inequality into 2 possible cases
x−1>1x−1<−1
Calculate
More Steps
Evaluate
x−1>1
Move the constant to the right side
x>1+1
Add the numbers
x>2
x>2x−1<−1
Cancel equal terms on both sides of the expression
x>2x<0
Find the union
x∈(−∞,0)∪(2,+∞)
x∈(−∞,0)∪(2,+∞),x−2≥04−2x<x−2,x−2<0
Solve the inequality
More Steps
Evaluate
x−2≥0
Move the constant to the right side
x≥0+2
Removing 0 doesn't change the value,so remove it from the expression
x≥2
x∈(−∞,0)∪(2,+∞),x≥24−2x<x−2,x−2<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∈(−∞,0)∪(2,+∞),x≥2x∈∅,x−2<0
Solve the inequality
More Steps
Evaluate
x−2<0
Move the constant to the right side
x<0+2
Removing 0 doesn't change the value,so remove it from the expression
x<2
x∈(−∞,0)∪(2,+∞),x≥2x∈∅,x<2
Find the intersection
x>2x∈∅,x<2
Find the intersection
x>2x∈∅
Find the union
x>2
Check if the solution is in the defined range
x>2,0≤x≤2
Solution
x∈∅
Alternative Form
No solution
Show Solution
