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oscnptdoExerci!e{6):

56

CtiapMr 2 Umtar Fquauons and I-mowiUm* In Om Variat>t*

2.1 Linear Equations and Formulas

Objectives

1    Sdv« Inear equatons in one

variablc.

2    Identify *dentities and contradictions.

3    Sohee tormulas tor specified variables.

^ Leammg ^ Strategy

As suggostod in tho To tho Student sectłon on page xvlll. arrange your notebook wlth four sections: Notes. Homework. Study Sheets, and Practice Tests. Remember to use color in your notes: red tor definitions and blue for rules and procedures. Organization and cotor codmg wili help you locate mportant items faster.

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Warm-Up

|1.4| 1. Tr.insl.jte to an cxprrssion. nine less th.in fivc limes a numbcr |1.4| 2. Eyjluate 1^ - 5*|;x = -3 I1.4| 3. Simplify. 2{3ni - 4) + 5{m ♦ 1)

InChaptcr 1, we reviewed rcal numbers and their propcrties and dcfincd constants, variables, cxpro*sions, cqu.itions, and incqualitics. We now move up the Algebra Pyraniid and considcr oquations Rocall thal an equation has an cqual sign

The Algebra Piframicł

I

Comtunb anJ V'uiiublrs

2.5.7 .x.y

Notę In thischapter,

* we cxploreoqu.il u ms

and inequalities; so we are at the top ot our Algebra Pyramld

An equation can be true or fatse For example, the equation 4 + 1 = 5 is łrue and tl*e equation 8 — 2 = 7 is false. lf an equation contains a variable for a missing numbcr, such as * + 3 = 9, our goal is to flnd ifcs solutionts) We can write those Solutions in a solution set

Definitions Solution: A number that makes an cquation true when it replaces the eariable in the equation.

Solution set A set contaimng all of the Solutions for a given equation.

Tor cxampJe. 6 is the solution to the equation x + 3 = 9 bccause rcplacing r with 6 makes the equatxm true

ar + 3 = 9

1

6 + 3 = 9 True

Notę By showing that the equatkin * * 3 ■ 9 is a true statement when a: is repłaced with 6, we have chccked that 6 is the solution for the 4 oquation

The solution set for this equation is {6}, or in sct-buildcr notation. {aja: = 6}. We fo-

Page 57 —>

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