{"id":23207,"date":"2023-03-07T07:03:51","date_gmt":"2023-03-07T07:03:51","guid":{"rendered":"https:\/\/www.booksofall.com\/cn\/?post_type=product&p=23207"},"modified":"2023-03-07T07:03:51","modified_gmt":"2023-03-07T07:03:51","slug":"open-resources-for-community-college-algebra","status":"publish","type":"product","link":"https:\/\/www.booksofall.com\/cn\/open-resources-for-community-college-algebra\/","title":{"rendered":"Open Resources for Community College Algebra"},"content":{"rendered":"

Chapter 1 Variables, Expressions, and Equations<\/b><\/p>\n

1.1 Variables and Evaluating Expressions\u00a0<\/b>Algebra<\/a> helps people solve mathematical problems that are just a bit too complicated to solve in your head. This book is meant to cover basic principles and skills that people need to become successful with algebra. The first things to learn about are\u00a0variables<\/i><\/a>,\u00a0algebraic expressions<\/i><\/a>,\u00a0equations<\/i><\/a>, and\u00a0inequalities<\/i><\/a>. In this section, we\u2019ll focus on variables and expressions. In the remainder of this chapter, we\u2019ll focus on\u00a0equations\u00a0<\/i>and\u00a0inequalities<\/i>.<\/p>\n

Figure 1.1.1: <\/b>Alternative Video Lesson<\/a><\/p>\n

1.1.1 Introduction to Variables\u00a0<\/b>When we want to represent an unknown or changing numerical quantity, we use a\u00a0variable<\/b>. For example, if you\u2019d like to discuss the gas mileage of various cars, you could use the symbol \u201cg\u201d as a variable to represent a car\u2019s gas mileage. The mileage might be 25 mpg<\/a>, 30 mpg, or something else. (\u201cmpg\u201d stands for \u201cmiles per gallon\u201d.) If we agree to use mpg for the units of measure, g might be a place holder for 25, 30, or some other number. Since we are using a variable and not a specific number, we can discuss gas mileage for Honda Civics<\/a>, Ford Explorers<\/a>, and all other makes and models at the same time, even though these makes and models have different gas mileages.<\/p>\n

When variables stand for actual physical quantities, it\u2019s good to use letters that clearly represent those quantities. For example, it\u2019s wise to use g to represent\u00a0g<\/i>as mileage. This helps the people who might read your work to understand it better.<\/p>\n

It is also important to identify what unit of measurement goes along with each variable you use, and clearly tell your reader this. For example, suppose you are working with g = 25. A car whose gas mileage\u00a0<\/i>is 25 mpg is very different from a car whose gas mileage is 25 kpg (kilometers per gallon<\/a>). So it would be important to tell readers that g represents gas mileage\u00a0in miles per gallon<\/i>.\u00a0<\/b><\/p>\n

Unless an algebra problem specifies which letter(s) to use, we may\u00a0choose\u00a0<\/i>which letter(s) to use for our variable(s). However\u00a0without\u00a0<\/i>any context to a problem, x, y, and z are the most common letters used as variables, and you may see these variables (especially x) a lot.<\/p>\n

Also note that the units we use are often determined indirectly by other information given in an algebra problem. For example, if we\u2019re told that a car has used so many\u00a0gallons\u00a0<\/i>of gas after traveling so many\u00a0miles<\/i>, then this suggests we should measure gas mileage in mpg.<\/p>\n

1.1.2 Algebraic Expressions<\/b><\/p>\n

An\u00a0algebraic expression\u00a0<\/b>is any combination of variables and numbers using arithmetic operations. The following are all examples of algebraic expressions:<\/p>\n

\"\"<\/p>\n

Note that this definition of \u201calgebraic expression\u201d does\u00a0not\u00a0<\/i>include anything with an equals sign in it.<\/p>\n

Example 1.1.3\u00a0<\/b>The expression:<\/p>\n

\"\"<\/p>\n

can be used to convert a temperature in degrees Fahrenheit to degrees Celsius. To do this, we need a Fahrenheit temperature, F. Then we can evaluate\u00a0<\/b>the expression. This means replacing its variable(s) (in this case, F) with specific numbers and finding the result as a single, simplified number.<\/p>\n

Let\u2019s convert the temperature 89 \u00b0F to the Celsius scale by evaluating the expression.<\/p>\n

\"\"
\n\"\"<\/p>\n

This shows us that 89 \u00b0F is equivalent to approximately 31.67\u00a0\u25e6<\/i>C.<\/p>\n

Warning 1.1.4 Correct Vocabulary. <\/b>The steps in Example 1.1.3 are not considered \u201csolving\u201d anything. \u201cSolving\u201d is a word you might be tempted to use, because in everyday English you are \u201cfinding an answer.\u201d In algebra, there is a special meaning for \u201csolving\u201d something, and that will come soon in Section 1.5. When we substitute values in for variables and then compute the result, the technical thing to say is we are \u201cevaluating an expression.\u201d<\/p>\n","protected":false},"excerpt":{"rendered":"