# 7.3: Can I Graph You, Too?

*This activity is intended to supplement Algebra I, Chapter 6, Lesson 6.*

## Probmem 1 - Introduction to Disjunction and Conjunction

Consider the equation . To solve, you would graph both sides of the equation as functions and ) and mark the solution as the area where the graphs intersect.

The same method can be applied to inequalities.

Press **APPS** and select the **Inequalz** app. Press any key to begin.

**Example 1**:

- Using graph the left side as . The absolute value function is located by pressing
**MATH**and selecting**abs(**. - Using graph the right side as . On the equals sign, press
**ALPHA**for the sign. Press**ZOOM**and select**ZoomStandard**. - Find the intersection points by pressing
**[TRACE]**and selecting**intersect**. Now just move the cursor to the intersection point and press**ENTER**three times. The solution is where the shading overlaps the graph of the absolute value function.

In this case, the solution is .

When an absolute value is less than a number, it is a **conjunction** because the solution is just one part of the graph.

**Example 2:**

- Using graph the left side as .
- Using graph the right side as . On the equals sign, press
**ALPHA**for the sign. Press**WINDOW**to choose appropriate window settings. - Find the intersection points.

In this case, the solution is **or** .

When an absolute value is greater than a number, it is a **disjunction** because the solution is two separate parts of the graph.

## Problem 2 - Application of Disjunction and Conjunction

For the problems below, write the inequalities as either a conjunction or disjunction, then solve for . Check your solution by graphing using the method described in Examples 1 and 2. Please use your graphing calculator to check your results.

**#1:**

**#2:**

**#3:**

**#4:**

## Problem 3 - Real World Application

One application of absolute value inequalities is engineering tolerance. Tolerance is the idea that an ideal measurement and an actual measurement can only differ within a certain range.

A bolt with a diameter has a tolerance range of to , while the hole that it fits into has a tolerance range of to .

How can you express the tolerances of both the bolt and the hole in terms of an absolute value inequality?