# Solving Linear Inequalities

Taught by videomathtutor
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Lesson Summary:

In this lesson on solving linear inequalities, the video math tutor provides a self-tutorial on how to solve typical linear inequalities, including double inequalities and compound linear inequalities, using methods such as number line graphs and interval notation. The properties of inequalities are also reviewed, and answers are presented in inequality notation, interval notation, and set notation. Additionally, the lesson covers how to translate English phrases into inequalities and solve word problems.

Lesson Description:

[NOTE: This video is only the first 23 minutes of the full lesson. Please visit my website to purchase/rent complete version] This lesson consists of providing you with a Self-Tutorial on how to solve typical linear inequalities of the form: ax + b > c (any of these symbols: <, >, ≤, ≥ can be used). The tutor goes over how to draw number line graphs. Also covered is the Double Inequality (a < x < b). Properties of Inequalities are reviewed. Answers are presented in Inequality Notation, Interval Notation, and Set Notation. Compound Linear Inequalities are solved and graphed. Finally, English Phrases are translated into inequalities and some Word Problems are solved.

• How do you solve linear inequalities?
• What is an inequality?
• What is a solution to an inequality and how do you find the solutions?
• How many solutions does an inequality have?
• How can you check to see if a value is a solution to an inequality?
• How can you determine if x = 1 is a solution to x + 2 < 5?
• How can you determine if y = 11 is a solution to 3 - y >= -7?
• How can you determine if A = -2 is a solution to 4A <= -8?
• Which values are solutions to the inequality 2x - 3 > 5?
• What is the definition of a linear inequality?
• What is the definition of the graph of a linear inequality?
• What does the graph of an inequality look like?
• How do you know whether to use open or closed dots, brackets, parentheses, and the infinity or negative infinity sign when writing and graphing linear inequalities on a number line?
• How do you graph x < a on a number line?
• What is set notation for a linear inequality?
• What is interval notation for a linear inequality?
• How do you write interval notation and graph x <= b on a number line?
• How do you write interval notation and graph x > c on a number line?
• How do you write interval notation and graph x >= d on a number line?
• How do you write interval notation and graph a < x < b on a number line?
• How do you write interval notation and graph a compound inequality on a number line?
• How do you write interval notation and graph c <= x < d on a number line?
• How do you write interval notation and graph e < x <= f on a number line?
• How do you write interval notation and graph g <= x <= h on a number line?
• #### Staff Review

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This lesson goes through some definitions of terms for inequalities and how to determine whether a value of a variable is a solution to an inequality. Also, this lesson goes through many different types of problems in which you need to graph an inequality on a number line, write set notation for the solution set, and write interval notation for the solution set. Several different example problems are shown in this video.