Solve for x |-1/(2+x)|<=1/6

Math
Remove the absolute value term. This creates a on the right side of the inequality because .
Set up the positive portion of the solution.
Solve the first inequality for .
Tap for more steps…
Move to the left side of the equation by subtracting it from both sides.
To write as a fraction with a common denominator, multiply by .
To write as a fraction with a common denominator, multiply by .
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
Tap for more steps…
Combine.
Combine.
Reorder the factors of .
Combine the numerators over the common denominator.
Simplify the numerator.
Tap for more steps…
Factor out of .
Tap for more steps…
Reorder the expression.
Tap for more steps…
Reorder and .
Reorder and .
Factor out of .
Factor out of .
Add and .
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 .
Tap for more steps…
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.
Interval Notation:
Interval Notation:
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.
Tap for more steps…
Test a value on the interval to see if it makes the inequality true.
Tap for more steps…
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 always true.
True
True
Test a value on the interval to see if it makes the inequality true.
Tap for more steps…
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 false.
False
False
Test a value on the interval to see if it makes the inequality true.
Tap for more steps…
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 always true.
True
True
Compare the intervals to determine which ones satisfy the original inequality.
True
False
True
True
False
True
The solution consists of all of the true intervals.
or
or
Set up the negative portion of the solution. When solving the negative portion of an inequality, flip the direction of the inequality sign.
Solve the second inequality for .
Tap for more steps…
Move to the left side of the equation by adding it to both sides.
To write as a fraction with a common denominator, multiply by .
To write as a fraction with a common denominator, multiply by .
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
Tap for more steps…
Combine.
Combine.
Reorder the factors of .
Combine the numerators over the common denominator.
Simplify the numerator.
Tap for more steps…
Multiply by .
Multiply by .
Add and .
Simplify with factoring out.
Tap for more steps…
Rewrite as .
Factor out of .
Factor out of .
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.
Multiply each term in by
Tap for more steps…
Multiply each term in by .
Multiply .
Tap for more steps…
Multiply by .
Multiply by .
Multiply by .
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 .
Tap for more steps…
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.
Interval Notation:
Interval Notation:
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.
Tap for more steps…
Test a value on the interval to see if it makes the inequality true.
Tap for more steps…
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.
Tap for more steps…
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.
Tap for more steps…
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
Compare the intervals to determine which ones satisfy the original inequality.
True
False
True
True
False
True
The solution consists of all of the true intervals.
or
or
Set up the intersection.
and ( or )
Use the rule to find the intersection.
The result can be shown in multiple forms.
Inequality Form:
Interval Notation:
Solve for x |-1/(2+x)|<=1/6

The Best MATH SOLVER APP

Are you looking app for solving your math tasks? Then this APP is the best option for you.

Learn math, check algebra homework and study for upcoming mathematics tests Useh the most learning math app in the world!
Our app is probably the best math problem-solving app for your.
Our math solver app provides help with a variety of problems including calculus, arithmetic, trigonometry, statistics, and algebra. Math app is the best math solver app that you can use on your Android or Ipone smartphone.

Scroll to top