5. Working with inequalities is similar to working with equations. A solution to a one-variable inequality is a value for the variable that makes the inequality true. The set of all solutions to an inequality is a set of numbers that all make the inequality true. The solution to a one-variable inequality is usually graphed on a number line. Most of the properties of equality can also be used to solve inequalities. The only exception is that when you multiply or divide both sides of an inequality by a negative number, you must reverse the direction of the inequality sign to produce an equivalent inequality.
Solve the inequality.
(a) Solve the inequality: .
(b) The manager at Super Fit is not adding members at the rate he wants so he decides to change his fee structure to see if that helps. His new fee structure reduces the one-time registration fee to $24 and raises the monthly fee to $24 a month. Solve the inequality to determine how many months it will take for a member to be paying more under the new plan than the old plan.