Chapter 8 - XYZ Custom Plus

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496<strong>Chapter</strong> 8 Linear Equations and InequalitiesGetting Ready for the Next SectionProblems under this heading, Getting Ready for the Next Section, are problems that you must be able to work to understandthe material in the next section. The problems below are exactly the types of problems you will see in the explanationsand examples in the next section.Simplify.119. 17 − 5120. 12 + (−2)121. 2 − 5122. 25 − 201210−35123. −2.4 + (−7.3)−9.7124. 8.1 + 2.710.8125. − 1 _2 + − 3 _4 _126. − 1_− 5 4 _− 5 6 6 + − 2 _3 127. 4(2 ⋅ 9 − 3) − 7 ⋅ 9128. 5(3 ⋅ 45 − 4) − 14 ⋅ 45129. 4(2a − 3) − 7a130. 5(3a − 4) − 14a−325a − 12a − 20131. −3 − _1 2 132. −5 − _1 3 133. _4 5 + 1 _10 + 3 _8 134. _310 + 7 _25 + 3 _4 _− 7 2 _− 163 _ 5140 _ 133100 135. Find the value of 2x − 3 when x is 5.7136. Find the value of 3x + 4 when x is −2.−2Maintaining Your SkillsFrom this point on, each problem set will contain a number of problems under the heading Maintaining Your Skills. Theseproblems cover the most important skills you have learned in previous sections and chapters. By working these problemsregularly, you will keep yourself current on all the topics we have covered and possibly need less time to study for testsand quizzes.137. 1 _8 − 1 _6 138. _x_− 1 24 8 − x _6 − x _24 139. 5 _9 − 4 _3 140. _x_− 7 9 9 − x _3 − 2x _9 141. − 7 _30 + 5 _28 _142. − 11105420 _ 1142 − 23 _+ 11_30
Addition Property of EqualityWhen light comes into contact with any object, it is reflected, absorbed, andtransmitted, as shown here.Reflected8.2ObjectivesA Check the solution to an equationby substitution.B Use the addition property ofequality to solve an equation.AbsorbedTransmittedFor a certain type of glass, 88% of the light hitting the glass is transmitted throughto the other side, whereas 6% of the light is absorbed into the glass. To find thepercent of light that is reflected by the glass, we can solve the equation88 + R + 6 = 100Solving equations of this type is what we study in this section. To solve an equationwe must find all replacements for the variable that make the equation a truestatement.ASolutions to EquationsDefinitionThe solution set for an equation is the set of all numbers that when used inplace of the variable make the equation a true statement.For example, the equation x + 2 = 5 has solution set {3} because when x is 3the equation becomes the true statement 3 + 2 = 5, or 5 = 5.Example 1Is 5 a solution to 2x − 3 = 7?Solution We substitute 5 for x in the equation, and then simplify to see if atrue statement results. A true statement means we have a solution; a false statementindicates the number we are using is not a solution.When x = 5the equation 2x − 3 = 7becomes 2(5) − 3 ≟ 710 − 3 ≟ 77 = 7 A true statementPractice Problems1. Is 4 a solution to 2x + 3 = 7?NoteWe can use a questionmark over the equalsigns to show that wedon’t know yet whether the twosides of the equation are equal.Because x = 5 turns the equation into the true statement 7 = 7, we know 5 is asolution to the equation.Example 2Is −2 a solution to 8 = 3x + 4?SolutionSubstituting −2 for x in the equation, we have2. Is _4 a solution to 8 = 3x + 4?38 ≟ 3(−2) + 48 ≟ −6 + 48 = −2 A false statementSubstituting −2 for x in the equation produces a false statement. Therefore,x = −2 is not a solution to the equation.Answers1. No 2. Yes8.2 Addition Property of Equality497
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Chapter 8 - XYZ Custom Plus

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