Learning Objectives:

__Math Tutoring on Solving Linear Inequalities in Two Variables__

When the equal sign in a **linear equation** is replaced with an **inequality **sign, a **linear inequality** is formed.

The **solution** for a **linear equation** consists of all **points x, y** that satisfy the equation. The solution forms a line. However, when we have a **linear inequality,** the solution consists of all the points that satisfy the **inequality** but the solution forms a region or half-plane with the line as a border. The line may or may not be included in the solution based upon the **inequality symbol**. Here are the **steps to graphing** the solution to a **linear inequality.**

**1. Graph the inequality** as if it was a line. However, if the **inequality symbol **is** < or ˃**, make a **dashed line** because the line will not be part of the solution. If the **inequality symbol **is** ≤ or ≥** make a solid line because the line will be part of the solution.

**2.** **Test a point** on either side of the line. If the coordinates of the point satisfy the original **inequality**, shade the same side of the line as the point. If the **inequality** is false we will shade the other side of the line. There is a shortcut if the **inequality** is solved for **y;** you can shade above the line for **˃**** or ****≥**. For **< or ≤** shade below the line.

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**Hook Questions:**

*1. **How can a linear equation be converted to linear inequality?*

*2. **What is the difference between solution for a linear equality and linear inequality?*

*3. **How to graph linear inequality?*

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