Graph x/(x+4)>=2

Graph x/(x+4)>=2
Subtract from both sides of the inequality.
Simplify .
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To write as a fraction with a common denominator, multiply by .
Combine and .
Combine the numerators over the common denominator.
Simplify the numerator.
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Apply the distributive property.
Multiply by .
Subtract from .
Factor out of .
Rewrite as .
Factor out of .
Rewrite as .
Move the negative in front of the fraction.
Find all the values where the expression switches from negative to positive by setting each factor equal to and solving.
Subtract from both sides of the equation.
Subtract from both sides of the equation.
Solve for each factor to find the values where the absolute value expression goes from negative to positive.
Consolidate the solutions.
Find the domain of .
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Set the denominator in equal to to find where the expression is undefined.
Subtract from both sides of the equation.
The domain is all values of that make the expression defined.
Use each root to create test intervals.
Choose a test value from each interval and plug this value into the original inequality to determine which intervals satisfy the inequality.
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Test a value on the interval to see if it makes the inequality true.
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Choose a value on the interval and see if this value makes the original inequality true.
Replace with in the original inequality.
The left side is less than the right side , which means that the given statement is false.
False
False
Test a value on the interval to see if it makes the inequality true.
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Choose a value on the interval and see if this value makes the original inequality true.
Replace with in the original inequality.
The left side is greater than the right side , which means that the given statement is always true.
True
True
Test a value on the interval to see if it makes the inequality true.
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Choose a value on the interval and see if this value makes the original inequality true.
Replace with in the original inequality.
The left side is less than the right side , which means that the given statement is false.
False
False
Compare the intervals to determine which ones satisfy the original inequality.
False
True
False
False
True
False
The solution consists of all of the true intervals.
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Name

Name four hundred seventy-two million three hundred seventy-seven thousand six hundred thirty-one

Interesting facts

  • 472377631 has 8 divisors, whose sum is 474495840
  • The reverse of 472377631 is 136773274
  • Previous prime number is 709

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 9
  • Sum of Digits 40
  • Digital Root 4

Name

Name one hundred eighty-three million four hundred seventy-one thousand one hundred eighty-two

Interesting facts

  • 183471182 has 16 divisors, whose sum is 290653440
  • The reverse of 183471182 is 281174381
  • Previous prime number is 307

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 9
  • Sum of Digits 35
  • Digital Root 8

Name

Name one billion three hundred fifty-one million nine hundred fifty-nine thousand eight hundred forty-two

Interesting facts

  • 1351959842 has 8 divisors, whose sum is 2028146256
  • The reverse of 1351959842 is 2489591531
  • Previous prime number is 11867

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 10
  • Sum of Digits 47
  • Digital Root 2