Solving Multi-Step Linear Inequalities Algebraically
The Substitution Property
The substitution property states that if two values are equal, then one value can replace the other in an equation or inequality.
Given: a < 5 and a = 4
Because a is equal to 4, 4 can replace a in the given inequality.
a < 5
4 < 5
The substitution property will be used as a tool to explain the properties of inequality. During the lesson on the properties of inequality, numerical values will be substituted for variables to explain the following properties:
- Transitive Property of Inequality
- Addition Property of Inequality
- Subtraction Property of Inequality
- Multiplication Property of Inequality
- Division Property of Inequality
Properties of Inequality
Before you begin solving multi-step linear inequalities, you should learn about the different properties of inequality. Being familiar with these properties will help you as you begin solving linear inequalities. This interactivity will cover these properties in detail. Click the player button to begin.
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Examples of the Properties of Inequality
In this interactivity, you will apply your knowledge of the Properties of Inequality as you work through some algebraic examples. These additional examples will help reinforce your understanding of the properties covered in the previous lesson. Click the player button to begin.
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How is graphing a strict inequality different from graphing a non-strict inequality?
A strict inequality is an inequality that includes < (less than) or > (greater than). When graphing a strict inequality on a number line, use an open circle. For example:
Number Line Graphs of Strict Inequalities
A non-strict inequality is an inequality that includes ≤ (less than or equal to) or ≥ (greater than or equal to). When graphing a non-strict inequality on a number line, use a closed circle. For example:
Number Line Graphs of Non-Strict Inequalities
Solving Linear Inequalities
This interactivity will focus on applying your knowledge of the properties of inequality in order to solve multi-step linear inequalities in one variable. Your knowledge of how to solve linear equations will also prove useful. Click the player button to begin.
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Solving Multi-Step Linear Inequalities Algebraically Review
Now that you have learned about the properties of inequality and how to solve multi-step linear inequalities algebraically, it is time to test your knowledge. This interactivity will help you review the information covered in this topic. Click the player button to get started.
Did you answer the content review questions incorrectly? Do you want more instruction or extra practice? If so, view the video Properties of Inequality from eMediaVASM.