Solving Multi-Step Equations: A Guide with Examples and Patterns for Consecutive Integers | Exams Algebra

3.4:SolvingMulti‐StepEquations  [Algebra1(X)]

HawaiiContentandPerformanceStandardsIII

 Standard10:Patterns,Functions,andAlgebra:SYMBOLICREPRESENTATION:Usesymbolicformstorepresent,

model,andanalyzemathematicalsituations.

 BenchmarkMA.AI.10.1:Solvelinearequationsandinequalitiesinonevariableusingavarietyofstrategies.

 BenchmarkMA.AI.10.3:Justifythestepsusedinsimplifyingexpressionsandsolvingequationsandinequalities.

CommonCoreStateStandardsforHighSchoolMathematics

 A.REI.1:Understandsolvingequationsasaprocessofreasoningandexplainthereasoning.

Explaineachstepinsolvingasimpleequationasfollowingfromtheequalityofnumbersassertedattheprevious

step,startingfromtheassumptionthattheoriginalequationhasasolution.Constructaviableargumentto

justifyasolutionmethod.

 A.REI.3:Solveequationsandinequalitiesinonevariable.

Solvelinearequationsandinequalitiesinonevariable,includingequationswithcoefficientsrepresentedby

letters.

Objectives:

 Tosolveproblembyworkingbackward.

 Tosolveequationsinvolvingmorethanoneoperation.



WorkBackwardtoSolveaProblem



WorkingBackward:

 Oneofmanystrategiesusedtosolveproblems(page142).

 Itismuchlikeretracingyourstepsbacktothestartingpoint.



Example1:WorkBackwardtoSolveaProblem

Solvethefollowingproblemsbyworkingbackward.



a.) Aftercashingherpaycheck,Tarapaidherfatherthe$20sheborrowed.She

thenspenthalfoftheremainingmoneyonaconcertticket.Sheboughtlunch

for$4.35andhad$10.5left.Whatwastheamountofthepaycheck?



Startattheendoftheproblemandundoeachstep.

StatementUndotheStatement

Shehad$10.55left$10.55

Sheboughtlunchfor$4.35$10.55+$4.35=$14.90

Shespenthalfofthemoneyonaconcertticket. $14.90x2=$29.80

Shepaidherfather$20$29.80+$20=$49.80

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3.4: Solving Multi‐Step Equations [Algebra 1(X)]

Hawaii Content and Performance Standards III  Standard 10: Patterns, Functions, and Algebra: SYMBOLIC REPRESENTATION: Use symbolic forms to represent, model, and analyze mathematical situations.  Benchmark MA.AI.10.1: Solve linear equations and inequalities in one variable using a variety of strategies.  Benchmark MA.AI.10.3: Justify the steps used in simplifying expressions and solving equations and inequalities. Common Core State Standards for High School Mathematics  A.REI.1: Understand solving equations as a process of reasoning and explain the reasoning. Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.  A.REI.3: Solve equations and inequalities in one variable. Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. Objectives:  To solve problem by working backward.  To solve equations involving more than one operation.

Work Backward to Solve a Problem

Working Backward:

 One of many strategies used to solve problems (page 142).

 It is much like retracing your steps back to the starting point.

Example 1: Work Backward to Solve a Problem

Solve the following problems by working backward.

a.) After cashing her paycheck, Tara paid her father the $20 she borrowed. She then spent half of the remaining money on a concert ticket. She bought lunch for $4.35 and had $10.5 left. What was the amount of the paycheck?

Start at the end of the problem and undo each step. Statement Undo the Statement She had $10.55 left $10. She bought lunch for $4.35 $10.55 + $4.35 = $14. She spent half of the money on a concert ticket. $14.90 x 2 = $29. She paid her father $20 $29.80 + $20 = $49.

b.) Danny took some rope with him on his camping trip. He used 32 feet of rope to tie his canoe to a log on the shore. He then gave one‐third of the remaining rope to some fellow campers who also needed to tie a canoe. The next night, he used half of the remaining rope to secure his tend during a thunderstorm. On the last day, he used 7 feet as a fish stringer to keep the fish that he caught. After the camping trip, he had 9 feet left. How much rope did he have at the beginning of the camping trip?

Solve Multi‐Step Equations

A multi‐step equation contains more than one operation. In order to

solve a multi‐step equation, you must work backwards to solve for the

variable using reverse order of operations (GEMDAS).

Steps to Solving Multi‐Step Equations

1. Simplify both sides of the equation, if necessary.

2. Locate the variable you want to solve.

3. Determine the order of operations occurring to the variable.

4. Undo each operation by using its inverse operation.

Example 2: Solve a Multi‐Step Equation Solve each equation. Then check your solution. a.) 7 ݉െ 17 ൌ 60 b.) 5 ݍെ 13 ൌ 37

Example 4: Write an Solve a Multi‐Step Equation Write an equation for each problem. Then solve the equation. a.) Two‐thirds of a number minus six is ‐10.

b.) Eight more than five times a number is negative 62.

Consecutive Integers

Consecutive integers are negative and positive whole numbers that are in

counting order (e.g., 1, 2, 3, 4, 5).

Pattern for Consecutive Integers:

1 st^ Number: n

2 nd^ Number: n + 1

3 rd^ Number: n + 2

Pattern for Consecutive ODD or EVEN Integers:

1 st^ Number: n

2 nd^ Number: n + 2

3 rd^ Number: n + 4

Example 5: Solve a Consecutive Integer Problem NUMBER THEORY. Write an equation for each problem below. Then solve the equation and answer the problem. a.) Find three consecutive even integers whose sum is ‐ 42.

b.) Find three consecutive odd integers whose sum is 57.

Solving Multi-Step Equations: A Guide with Examples and Patterns for Consecutive Integers, Exams of Algebra

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Download Solving Multi-Step Equations: A Guide with Examples and Patterns for Consecutive Integers and more Exams Algebra in PDF only on Docsity!

3.4: Solving Multi‐Step Equations [Algebra 1(X)]

Work Backward to Solve a Problem

Working Backward:

 One of many strategies used to solve problems (page 142).

 It is much like retracing your steps back to the starting point.

Example 1: Work Backward to Solve a Problem

A multi‐step equation contains more than one operation. In order to

solve a multi‐step equation, you must work backwards to solve for the

variable using reverse order of operations (GEMDAS).

Steps to Solving Multi‐Step Equations

1. Simplify both sides of the equation, if necessary.

2. Locate the variable you want to solve.

3. Determine the order of operations occurring to the variable.

4. Undo each operation by using its inverse operation.

Consecutive integers are negative and positive whole numbers that are in

counting order (e.g., 1, 2, 3, 4, 5).

Pattern for Consecutive Integers:

1 st^ Number: n

2 nd^ Number: n + 1

3 rd^ Number: n + 2

Pattern for Consecutive ODD or EVEN Integers:

1 st^ Number: n

2 nd^ Number: n + 2

3 rd^ Number: n + 4