Move all terms containing variables to the left side of the inequality.

Move to the left side of the inequality because it contains a variable.

Combine fractions with similar denominators.

Simplify the expression.

Subtract from .

Move the negative in front of the fraction.

Subtract from both sides of the inequality.

Solve for .

Multiply each term by and simplify.

Multiply each term in by .

Cancel the common factor of .

Move the leading negative in into the numerator.

Cancel the common factor.

Rewrite the expression.

Rewrite so is on the left side of the inequality.

Divide each term by and simplify.

Divide each term in by . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

Cancel the common factor of .

Cancel the common factor.

Divide by .

Divide by .

Find the domain of .

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

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.

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 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 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.

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

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.

Use the inequality to build the set notation.

Convert to Set Notation 7-2/b<=5/b