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# ZingPath: Representing Linear Inequalities and Two Quantities

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## Representing Linear Inequalities and Two Quantities

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Math Foundations

### Learning Made Easy

Graphing linear inequalities in one variable on the number line is explained.

### Now You Know

After completing this tutorial, you will be able to complete the following:

• Translate verbal sentences into linear inequalities in one variable
• Graph linear inequalities in one variable on the number line.
• Write linear inequalities in one variable represented by a graph.

### Everything You'll Have Covered

In this Activity Object, learners will explore single or compound inequalities. Note that double inequalities are also called compound inequalities.

Single Inequalities

An inequality is a mathematical sentence that uses symbols such as <, ?, >, or ? to compare two quantities. The inequality sign expresses that the quantity on the left hand side is the less than, greater than, less than or equal to, or greater than or equal to the quantity on the right hand side.

x < 3: x is less than 3.

x ? 3: x is less than or equal to 3.

x > 3: x is greater than 3.

x ? 3: x is greater than or equal to 3.

Compound inequalities

Compound inequalities are two separate inequalities joined by "and" or "or."

?3 < x < 10: All numbers between -3 and 10 OR all numbers greater than ?3 and less than 10. (In the Activity Object, these inequalities are called double inequalities.)

x > 0 and x ? 2: All numbers that are greater 0 and greater than or equal to2.

x > 0 or x ? ?2: All numbers that are greater 0 or less than or equal to ?2.

Open circle vs. closed circle

When we graph inequalities on a number line, circles are used to show if a number is included or not. An open circle shows that the number is not included, while a closed circle includes the number.

For example,

Interval notation

When we write inequalities with interval notation, parenthesis and square brackets are used.

For example,

Consider the inequality x > 5: Using interval notation, the group of numbers would be written as .

The parenthesis on the left means the set of numbers starts at the real number which is immediately to the right of 5 on the number line; that is, 5 is excluded from the group. Because this group of numbers continues all the way to positive infinity, the positive infinity symbol is used, which is always accompanied by a parenthesis.

Now consider the inequality x ? 5: Using interval notation, the group of numbers would be written as .

The square bracket on the left means that the set of numbers starts on the number line with 5 and that 5 is included in the solution set. Again, the infinity symbol is always accompanied by a parenthesis.

Next we can examine the inequality 3 ? x < 6.

Using interval notation, the group of numbers would be written as .

The square bracket on the left means that the set of numbers starts on the number line with 3 and that 3 is included in the solution set. The parenthesis on the right means that the set of numbers finishes close to 6, without including 6.

### Tutorial Details

 Approximate Time 30 Minutes Pre-requisite Concepts Students should know how to solve linear equations. Course Math Foundations Type of Tutorial Skills Application Key Vocabulary compound inequality, inequality, linear inequality