Algebra
Calculus
Trigonometry
Matrix
Question
Solve the inequality
x>10
Alternative Form
x∈(10,+∞)
Evaluate
x−105x2≥3
Find the domain
More Steps
Evaluate
x−10=0
Move the constant to the right side
x=0+10
Removing 0 doesn't change the value,so remove it from the expression
x=10
x−105x2≥3,x=10
Move the expression to the left side
x−105x2−3≥0
Subtract the terms
More Steps
Evaluate
x−105x2−3
Reduce fractions to a common denominator
x−105x2−x−103(x−10)
Write all numerators above the common denominator
x−105x2−3(x−10)
Multiply the terms
More Steps
Evaluate
3(x−10)
Apply the distributive property
3x−3×10
Multiply the numbers
3x−30
x−105x2−(3x−30)
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−105x2−3x+30
x−105x2−3x+30≥0
Separate the inequality into 2 possible cases
{5x2−3x+30≥0x−10>0{5x2−3x+30≤0x−10<0
Solve the inequality
More Steps
Evaluate
5x2−3x+30≥0
Move the constant to the right side
5x2−3x≥0−30
Add the terms
5x2−3x≥−30
Evaluate
x2−53x≥−6
Add the same value to both sides
x2−53x+1009≥−6+1009
Evaluate
x2−53x+1009≥−100591
Evaluate
(x−103)2≥−100591
Calculate
x∈R
{x∈Rx−10>0{5x2−3x+30≤0x−10<0
Solve the inequality
More Steps
Evaluate
x−10>0
Move the constant to the right side
x>0+10
Removing 0 doesn't change the value,so remove it from the expression
x>10
{x∈Rx>10{5x2−3x+30≤0x−10<0
Solve the inequality
More Steps
Evaluate
5x2−3x+30≤0
Move the constant to the right side
5x2−3x≤0−30
Add the terms
5x2−3x≤−30
Evaluate
x2−53x≤−6
Add the same value to both sides
x2−53x+1009≤−6+1009
Evaluate
x2−53x+1009≤−100591
Evaluate
(x−103)2≤−100591
Calculate
x∈/R
{x∈Rx>10{x∈/Rx−10<0
Solve the inequality
More Steps
Evaluate
x−10<0
Move the constant to the right side
x<0+10
Removing 0 doesn't change the value,so remove it from the expression
x<10
{x∈Rx>10{x∈/Rx<10
Find the intersection
x>10{x∈/Rx<10
Find the intersection
x>10x∈/R
Find the union
x>10
Check if the solution is in the defined range
x>10,x=10
Solution
x>10
Alternative Form
x∈(10,+∞)
Show Solution
