Algebra
Calculus
Trigonometry
Matrix
Question
Solve the inequality
x∈∅
Alternative Form
No solution
Evaluate
x2−x−2<101
Find the domain
More Steps
Evaluate
{x2≥0x−2≥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
{x∈Rx−2≥0
Calculate
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∈Rx≥2
Find the intersection
x≥2
x2−x−2<101,x≥2
Calculate
∣x∣−x−2<101
Separate the inequality into 2 possible cases
x−x−2<101,x≥0−x−x−2<101,x<0
Evaluate
More Steps
Evaluate
x−x−2<101
Move the expression to the left side
x−x−2−101<0
Change the signs on both sides of the inequality and flip the inequality sign
x−2−x+101>0
Move the expression to the right side
x−2>x−101
Separate the inequality into 2 possible cases
x−2>x−101,x−101≥0x−2>x−101,x−101<0
Solve the inequality
More Steps
Solve the inequality
x−2>x−101
Square both sides of the inequality
x−2>(x−101)2
Move the expression to the left side
x−2−(x−101)2>0
Calculate
56x−100201−x2>0
Move the constant to the right side
56x−x2>0−(−100201)
Add the terms
56x−x2>100201
Evaluate
x2−56x<−100201
Add the same value to both sides
x2−56x+259<−100201+259
Evaluate
x2−56x+259<−2033
Evaluate
(x−53)2<−2033
Calculate
x∈/R
x∈/R,x−101≥0x−2>x−101,x−101<0
Solve the inequality
More Steps
Evaluate
x−101≥0
Move the constant to the right side
x≥0+101
Removing 0 doesn't change the value,so remove it from the expression
x≥101
x∈/R,x≥101x−2>x−101,x−101<0
Since the left-hand side is always positive or 0,and the right-hand side is always negative,the statement is true for any value of x
x∈/R,x≥101x∈R,x−101<0
Solve the inequality
More Steps
Evaluate
x−101<0
Move the constant to the right side
x<0+101
Removing 0 doesn't change the value,so remove it from the expression
x<101
x∈/R,x≥101x∈R,x<101
Find the intersection
x∈/Rx∈R,x<101
Find the intersection
x∈/Rx<101
Find the union
x<101
x<101,x≥0−x−x−2<101,x<0
Evaluate
More Steps
Evaluate
−x−x−2<101
Move the expression to the left side
−x−x−2−101<0
Change the signs on both sides of the inequality and flip the inequality sign
x−2+x+101>0
Move the expression to the right side
x−2>−x−101
Separate the inequality into 2 possible cases
x−2>−x−101,−x−101≥0x−2>−x−101,−x−101<0
Solve the inequality
More Steps
Solve the inequality
x−2>−x−101
Square both sides of the inequality
x−2>(−x−101)2
Move the expression to the left side
x−2−(−x−101)2>0
Calculate
54x−100201−x2>0
Move the constant to the right side
54x−x2>0−(−100201)
Add the terms
54x−x2>100201
Evaluate
x2−54x<−100201
Add the same value to both sides
x2−54x+254<−100201+254
Evaluate
x2−54x+254<−2037
Evaluate
(x−52)2<−2037
Calculate
x∈/R
x∈/R,−x−101≥0x−2>−x−101,−x−101<0
Solve the inequality
More Steps
Evaluate
−x−101≥0
Move the constant to the right side
−x≥0+101
Removing 0 doesn't change the value,so remove it from the expression
−x≥101
Change the signs on both sides of the inequality and flip the inequality sign
x≤−101
x∈/R,x≤−101x−2>−x−101,−x−101<0
Since the left-hand side is always positive or 0,and the right-hand side is always negative,the statement is true for any value of x
x∈/R,x≤−101x∈R,−x−101<0
Solve the inequality
More Steps
Evaluate
−x−101<0
Move the constant to the right side
−x<0+101
Removing 0 doesn't change the value,so remove it from the expression
−x<101
Change the signs on both sides of the inequality and flip the inequality sign
x>−101
x∈/R,x≤−101x∈R,x>−101
Find the intersection
x∈/Rx∈R,x>−101
Find the intersection
x∈/Rx>−101
Find the union
x>−101
x<101,x≥0x>−101,x<0
Find the intersection
0≤x<101x>−101,x<0
Find the intersection
0≤x<101−101<x<0
Find the union
−101<x<101
Check if the solution is in the defined range
−101<x<101,x≥2
Solution
x∈∅
Alternative Form
No solution
Show Solution
