Introduction to Solving Single- and Multi-Step Inequalities

What You Will Learn to Do: Solve Single-Step and Multi-Step Inequalities

Sometimes, there is a range of possible values to describe a situation. When you see a sign that says “Speed Limit [latex]25[/latex],” you know that it doesn’t mean that you have to drive at exactly a speed of [latex]25[/latex] miles per hour (mph). This sign means that you are not supposed to go faster than [latex]25[/latex] mph, but there are many legal speeds you could drive, such as [latex]22[/latex] mph, [latex]24.5[/latex] mph or [latex]19[/latex] mph. In a situation like this, which has more than one acceptable value, inequalities, rather than equations, are used to represent the situation.

Solving multi-step inequalities is very similar to solving equations—what you do to one side, you need to do to the other side, in order to maintain the “balance” of the inequality. The Properties of Inequality can help you understand how to add, subtract, multiply, or divide within an inequality.

In particular, you will learn how to:

  • Represent inequalities on a number line
  • Represent inequalities using interval notation
  • Describe solutions to inequalities
  • Solve single-step inequalities
  • Solve multi-step inequalities


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