# Solve the Inequality for x (3x+8)/(x-4)>=0

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.

Divide each term in by and simplify.

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Divide each term in by .

Simplify the left side.

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Cancel the common factor of .

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Cancel the common factor.

Divide by .

Simplify the right side.

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Move the negative in front of the fraction.

Add to 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.

Add to 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 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

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

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

The result can be shown in multiple forms.

Inequality Form:

Interval Notation:

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