Standard+2.1d-cg

===Standard 1.1. 2.1d Use algebraic, interval, and set notations to specify the domain and range of functions of various typesThe student will use the proper notation to specify the domain and range of functions=== Modeling refers to actually being able to translate the equation into a visual picture. Writing a linear equation requires a person to understand how letters (called variables) interact with numbers by operations. Solving these problems involves finding the number that makes the equation true. These linear equations are actually lines on a coordinate plane. There are several ways to solve these types problem.

Example Problems for Standard 1.1a
Below are two example problems. They range from easy to difficult. 4x - 10 = 18**
 * Problem 1-Easy**
 * What value of x makes this equation true?

To answer this question, you must understand what the equation is stating. It is saying a number is multiplied to 4. This answer is then subtracted by 10 and the result is 18. In order to find the number, we must complete inverse operations. This means completing the opposite operation and working in reverse. See the steps below.

4x - 10 = 18 __+10 +10__ Add 10 to both sides of the equal sign __4__x = __28__ 4 4 Divide 4 to both sides of the equal sign x = 7


 * Problem 1 - Difficult**
 * Stacey delivers newspapers. She earns $15 each week plus $0.50 for each customer on her route. Write an equation she can use to find c, the number of customers she needs to earn exactly $25 each week?**

This question is only difficult because it is asking you to create an equation. It also is a word problem which is often harder for most students. In order to answer this question, think about what operations you have to use to get how much Stacy earns. This helps to create the equation. Well, Stacy makes 15 a week to start. But she also gets .50 for each customer. Well, to find out how much she gets if she had 10 customers, we would multiply .50 by 10 customers. We still would have to add 15 to get her amount. Let's see, we multiplied and added. Let's write an equation in words then replace the words with letters and numbers.

Stacy's weekly pay = .50 x customers + 15 $25 = .50c + 15

Podcast for Standard 1.1a
Below is a tutorial on understanding two-step equations and how to solve the problems.