How to Identify and Solve Inequality Problems or Inequalities

The number of people in this photograph is greater than one.

In math, an inequality describes a situation in which one quantity is less than or greater than another. In order to identify an inequality, you must look for a less than or greater than sign. Inequalities are a way of describing boundaries; when you solve an inequality, you do not get an answer that corresponds to a specific value. Instead, the solution to an inequality corresponds to a range of values.

Things You'll Need

• Paper
• Pencil

Instructions

1. Examine the expression. If it has a ">" or "<" symbol, it is an inequality. If you are faced with a word problem, scan for the words "greater than" or "less than." These translate into ">" and "<", respectively.

2. Isolate the variable in the equality by adding or subtracting it to both sides. For example:

   7 - 5x > 6x - 15

   7 - 11x > -15

   Here, 6x was subtracted from both sides.

3. Add or subtract all other terms from the side with the variable, leaving only the variable term. For example:

   7 - 11x > -15

   -11x > -22

   Here, 7 was subtracted from both sides.

4. Divide both sides by the coefficient of your variable, leaving only the variable on one side. If you multiply or divide by a negative number in this step, invert the inequality. For example:

   -11x > -22

   x < 2

   Because you divide by -11, you must invert the inequality. The solution here is read "x is less than 2." This describes all the values of x that satisfy the inequality.

Tips & Warnings

• If the less than or greater than signs have a line under them, they are read as "less than or equal to" or "greater than or equal to."