How to Solve Inequalities With Brackets or Parenthesis

An inequality is a math equation where two given values are not equal. Essentially, it is an equation where the equal sign has been replaced by an inequality sign, such as "<" or ">" symbols. In order to solve an inequality problem that has parenthesis or brackets, you must understand the order of operations used to solve the problem. The acronym PEMDAS can help you remember what operation to do first. PEMDAS stands for Parenthesis, Exponents, Multiplication and Division and Addition and Subtraction.

Instructions

1. Write the equation out so that you can clearly read it with sufficient space between all symbols and numbers.

2. Remove the parenthesis or brackets first. In the United States, parenthesis are commonly used, whereas in the United Kingdom, brackets are commonly used. They have the same significance, and anything inside either parenthesis or brackets must be removed first. For instance, in the equation 2(3x-4)+6>12+4x you would multiple 2 x 3x and 2 x -4 first, leaving 6x-8+6>12+4x.

3. Simply the equation by adding or subtracting like values. In the example above, you would simpilfy to 6x-2>12+4x.

4. Add or subtract to get all variables on one side and all known values on the other side. Again, in our example, you would first add 2 to both sides of the equation leaving 6x > 14+4x. Then subtract 4x from both sides leaving 2x > 14.

5. Divide both sides by 2 in the example in order to get the variable (x) alone on one side of the equation leaving x > 7.

References

• Purple Math: The Order of Operations
• Mathsteacher.com: Inequalities Containing Brackets
• Math Motivation: Solving Inequalities