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 .

Multiply and .

Multiply by .

Multiply and .

Multiply by .

Combine the numerators over the common denominator.

Simplify the numerator.

Multiply by .

Add and .

Multiply each term by and simplify.

Convert the inequality to an equation.

Multiply each term in by .

Cancel the common factor of .

Factor out of .

Cancel the common factor.

Rewrite the expression.

Combine and .

Rewrite the equation as .

Multiply both sides of the equation by .

Simplify both sides of the equation.

Simplify .

Cancel the common factor of .

Cancel the common factor.

Rewrite the expression.

Cancel the common factor of .

Factor out of .

Cancel the common factor.

Rewrite the expression.

Simplify .

Cancel the common factor of .

Factor out of .

Cancel the common factor.

Rewrite the expression.

Multiply and .

Multiply by .

Set the denominator in equal to to find where the expression is undefined.

Divide each term by and simplify.

Divide each term in by .

Cancel the common factor of .

Cancel the common factor.

Divide by .

Divide by .

The domain is all values of that make the expression defined.

Use each root to create test intervals.

Test a value on the interval to see if it makes the inequality true.

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 not 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.

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.

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 not greater 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.

The result can be shown in multiple forms.

Inequality Form:

Interval Notation:

Solve for x 3/(5x)+1/(6x)>2/3