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Algebra-1

You will translate and then graph verbal sentences into linear inequalities in one variable and write linear inequalities in one variable represented by a graph.

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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 the graph.

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 to 2.

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,

The following graph represents x ? 3.

Approximate Time | 30 Minutes |

Pre-requisite Concepts | Learners should be familiar with inequality and numbers on the number line. |

Course | Algebra-1 |

Type of Tutorial | Guided Discovery |

Key Vocabulary | inequality, linear inequality, linear inequality in one variable |