# 2.2: Algebra Review

$$\newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} }$$ $$\newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}}$$$$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\kernel}{\mathrm{null}\,}$$ $$\newcommand{\range}{\mathrm{range}\,}$$ $$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$ $$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}[1]{\| #1 \|}$$ $$\newcommand{\inner}[2]{\langle #1, #2 \rangle}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\kernel}{\mathrm{null}\,}$$ $$\newcommand{\range}{\mathrm{range}\,}$$ $$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$ $$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}[1]{\| #1 \|}$$ $$\newcommand{\inner}[2]{\langle #1, #2 \rangle}$$ $$\newcommand{\Span}{\mathrm{span}}$$$$\newcommand{\AA}{\unicode[.8,0]{x212B}}$$

## Introduction

In section 1.2 (Mathematics and Scientific Communication) we went over how algebraic equations can be derived from theoretical equations, and these algebraic equations can be solved for a an unknown variable.  Once this is done, the mathematical values of the known variables can be substituted in and the equation can be arithmetically solved for a numerical answer.

We are now going to look at some mathematical operations that can be performed on both algebraic and arithmetic equations that maintain an equality.

Lets look at a simple equivalence relationship.  If A= 6 calories and B= 6 calories, then algebriacally,

A=B

## Algebraic Operations that Maintain an Equivalence

The following operations are commonly used to solve algebraic equations for specific variables.  For these to work, they must maintain the equivalence statement.

1. Adding the same value to both sides of an equivalence statement

if $A=B \nonumber$ then $A+C=B+C$

1. Subtracting the same value to both sides of an equivalence statement

if $A=B \nonumber$ then $A-C=B-C$

1. Multiplying same value to both sides of an equivalence statement

if $A=B \nonumber$  then $A(C)=B(C)$
(we often use parenthesis to indicate multiplication, but sometimes omit them)

AC=BC

1. Dividing same value into both sides of an equivalence statement

if $A=B \nonumber$ then  $\frac{A}{C}=\frac{B}{C}$

5. Multiplying and dividing by the same number does not change the value.

if $C=A(B)\ \\ then \\ C= A(B)(\frac{D}{D}) \\ so \\ C=AD\left ( \frac{B}{D} \right )=BD\left ( \frac{A}{D} \right )=AB$

## Test Yourself

Homework: Section 2.2

Activity $$\PageIndex{1}$$

NOTE: The step by step worked out solutions to these questions can be found in homework section 2.2 Algebra Review

## Contributors and Attributions

Robert E. Belford (University of Arkansas Little Rock; Department of Chemistry). The breadth, depth and veracity of this work is the responsibility of Robert E. Belford, rebelford@ualr.edu. You should contact him if you have any concerns. This material has both original contributions, and content built upon prior contributions of the LibreTexts Community and other resources, including but not limited to:

• Vincent Belford (H5P interactive modules)

This page titled 2.2: Algebra Review is shared under a not declared license and was authored, remixed, and/or curated by Robert Belford.