3.0 Introduction

If we carefully placed more rocks of equal weight on both sides of this formation, it would still balance. Similarly, the expressions in an equation remain balanced when we add the same quantity to both sides of the equation. In this chapter, we will solve equations, remembering that what we do to one side of the equation, we must also do to the other side.

This is a photo of several rocks carefully stacked to achieve balance.
Figure 3.0.1 : The rocks in this formation must remain perfectly balanced around the center for the formation to hold its shape Photo by Robert Anasch Unsplash License

Mathematical formulas model phenomena in every facet of our lives. They are used to explain events and predict outcomes in fields such as transportation, business, economics, medicine, chemistry, engineering, and many more. In this chapter, we will apply our skills in solving equations to solve problems in a variety of situations.

A photo of cars on two directions with different flow.
Figure 3.0.2 :Sophisticated mathematical models are used to predict traffic patterns on our nation’s highways. Photo  by Derek Lee  Unsplash License

Graphs are found in all areas of our lives—from commercials showing you which cell phone carrier provides the best coverage, to bank statements and news articles, to the boardroom of major corporations. In this chapter, we will study the rectangular coordinate system, which is the basis for most consumer graphs. We will look at linear graphs, slopes of lines, equations of lines, and linear inequalities.

This is a drawing of a graph. The x-axis ranges from 1994 through 2010 in two-year increments. The y-axis is labeled 0 to 30 million in increments of 5 millon per year. The y-axis is labeled “Annual Vehicle Sales (MM/year)” There are three line graphs. The first shows the annual sale of gas motorcyles from 5 million in 1994 to about 15 million in 2010. The next line is a green line labled EV for electric vehicles. It shows sales were null from 1994 through 2002, but they quickly rose to more than 25 million in sales per year. The last line is labeled gas cars and starts at 0 in 1994 and slowly rises from 2002 to 2010 to just over 10 million.
Figure 3.0.3: This graph illustrates the annual vehicle sales of gas motorcycles, gas cars, and electric vehicles from 1994 to 2010. It is a line graph with x- and y-axes, one of the most common types of graphs. Image by Steve Jurvetson CC-BY-2.0

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Fanshawe Pre-Health Sciences Mathematics 1 Copyright © 2022 by Domenic Spilotro, MSc is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License, except where otherwise noted.

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