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Solving Multi-StepEquationsby: Mike KowalskiClick for next slideClick for next slide
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Learning Objectives andStandardsTo be able to solve multi-step linear equations,and be able to explain the reasoning behindthe process used.CCSS: HSA-REI.A.1: Explain each step insolving a simple equation as following from theequality of numbers asserted at the previousstep, starting from the assumption that theoriginal equation has a solution. Construct aviable argument to justify a solution method.Click for next slideClick for next slide
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Table of ContentsWarm upProperties of EqualitySolving StrategiesTime to Balance!Google formReferencesClick for next slideClick for next slide
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Warm UpPerform the indicated operation.(click for next problem and answers)Problems: Answers:3*-8 -24-6+7 1-4-3 -7-15/-5 32+(-2) 0Click for next slideClick for next slide
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Warm UpHow’d you do?If you got most right move on to the next slide.If you need a little more practice check outthis video or this one.Click for next slideClick for next slide
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Properties of EqualityThese allow us tosolve an equation.We can think of anequation like abalance.It’s our job to makesure the balance stayseven, so our equationsstays equal.Click for next slideClick for next slide
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Properties of EqualityIf we don’t use theproperties of equalityour balance will not beeven.If we don’t keep ourbalance even, ourequation is no longertrue.Click for next slideClick for next slide
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Properties of EqualityThese are the properties weare going to use today:Addition Property ofEqualitySubtraction Property ofEqualityMultiplication Property ofEqualityDivision Property of Equality Click for next slideClick for next slide
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Properties of EqualityAddition Property ofEqualityIf a = b then a + c = b + cIn English: If we know anequation is true we can addthe same thing to bothsides.As long as we do the samething to both sides ourequation will stay balanced! Click for next slideClick for next slide
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Properties of EqualitySubtraction Property ofEqualityIf a = b then a - c = b - cIn English: If we know anequation is true we cansubtract the same thingfrom both sides.As long as we do the samething to both sides ourequation will stay balanced! Click for next slideClick for next slide
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Properties of EqualityMultiplication Property ofEqualityIf a = b then a*c =b*cIn English: If we know anequation is true we canmultiply both sides by thesame thing.As long as we do the samething to both sides ourequation will stay balanced! Click for next slideClick for next slide
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Properties of EqualityDivision Property of EqualityIf a = b and c≠0 (becauseyou can’t divide by 0), thena/c = b/cIn English: If we know anequation is true we canmultiply both sides by thesame thing.As long as we do the samething to both sides ourequation will stay balanced! Click for next slideClick for next slide
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Properties of EqualityNow that we know theProperties of Equalitywe can put them towork.Click for next slideClick for next slide
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Solving StrategiesLike the tools seenhere, we need tools tohelp us solveequations.Solving strategies areour tools.Click for next slideClick for next slide
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Solving StrategiesTo solve an equationour goal is to get thevariable by itself.To do that we aregoing to use theproperties of equalitydiscussed earlier andsome of these solvingstrategies.Click for next slideClick for next slide
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Solving StrategiesOne strategy is to get thevariable on one side of theequal sign first.You may not have to do thisfor every equation, but it’s agood thing to check.Variables can be moved fromone side of an equation toanother by using the additionand subtraction properties ofequality.Click for next slideClick for next slide
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Solving StrategiesOnce the variable is on oneside a good strategy to use is toeliminate numbers in theequation by working the orderof operations backwards.Do you remember the order ofoperations?PEMDAS which stands forParenthesis, Exponents,Multiply, Divide, Add, andSubtract!See this video for moreClick for next slideClick for next slide
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Solving StrategiesSo if we wanted to eliminate piecesfrom our equations using the order ofoperations backwards the first thing Ishould get rid of is addition andsubtraction.We can do that using the addition andsubtraction properties of equality.In order to eliminate addition from myequation I’m going to have to use thesubtraction property of equality.In order to eliminate subtraction frommy problem I’m going to have to usethe addition property of equality.Click for next slideClick for next slide
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Solving StrategiesThe next thing we can focus oneliminating is multiplication ordivision.We can do that using themultiplication and division propertiesof equality.In order to eliminate multiplicationfrom my equation I’m going to haveto use the division property ofequality.In order to eliminate division frommy problem I’m going to have to usethe multiplication property ofequality.Click for next slideClick for next slide
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Solving StrategiesRemember when you’reusing these strategies andthe properties of equality, it’sall about balance!If we don’t do the same thingto both sides, we’re notkeeping our equationbalanced.If our equation doesn’t staybalanced, we won’t end upwith the right answer.Click for next slideClick for next slide
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Time to Balance!Click for next slideClick for next slide
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Time to Balance!For this part we are going to try tosolve an equation while keeping ourscale balanced.You are going to need to click on thebullet you think is the correct step inorder to solve the equation.If you make the correct choice youwill be directed to the next step.If you make an incorrect choice youwill need to go back and try again.Ready to balance?!?Click for next slideClick for next slide
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Time to Balance!Solve the followingequation: 5x +3 = 3x -7I would subtract 3 from the left sideI would divide both sides by 5I would subtract 3x from both sides
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Time to Balance!Oops!You forgot to do the samething on both sides.Remember the subtractionproperty of equality says wemust subtract the samething from both sides of theequation.Click the arrow to take youback to the problem.Back to the problemBack to the problem
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Time to Balance!Oops!You forgot our solvingstrategies.We want to collect ourvariable on one side ofthe equation first.Click the arrow to takeyou back to theproblem.Back to the problemBack to the problem
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Time to Balance!Nice job! You used thesubtraction property of equalityto get your variable on one sideof the equation.Now for the next step.Continue solving 2x + 3 = -7I would divide both sides by 2I would subtract 3 from bothsidesI would add three to both sides
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Time to Balance!Oops!You forgot our solvingstrategies.We want to work the order ofoperation backwards.We need to take care ofaddition and subtractionbefore division.Click the arrow to take youback to the problem.Back to the problemBack to the problem
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Time to Balance!Oops!In order to solve we needto undo what’s in ourproblem.Since there’s already a + 3in the problem to get rid ofit we would need to do theopposite.Click the arrow to take youback to the problem.Back to the problemBack to the problem
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Time to Balance!Nice job! You used thesubtraction property of equalityto eliminate the +3Now for the next step.Continue solving 2x = -10I would divide both sides by 2I would divide the left side by 2I would divide both sides by -10
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Time to Balance!Oops!You forgot to do the samething on both sides.Remember the divisionproperty of equality sayswe need to divide bothsides by the same thing.Click the arrow to take youback to the problem.Back to the problemBack to the problem
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Time to Balance!Oops!If we’re trying to get thevariable by itself we need tofocus on the side of theequation with the variable.Since the -10 is already on theother side of the equation shiftyour focus back to the otherside and see if there’ssomething you can do.Click the arrow to take youback to the problem.Back to the problemBack to the problem
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Time to Balance!Nice job! You used the divisionproperty of equality to eliminatethe 2 multiplying the xYou solved the equationx = -5Since we got the variable byitself we know we’re done!You can use these samestrategies to solve anyequation.Click for next slideClick for next slide
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Google FormNow that you’ve seen the properties ofequality in action it’s your turn to try them out.Solve the problems on this Google Form topractice using the properties of equality tosolve equations.Once you’re done click submit so your resultscan be collected.Click for next slideClick for next slide
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You made it!Thanks for using myinteractive powerpoint.I hope you learned alot about solvingequations.Layla’s tuckered outfrom all this solving.Time for a nap.
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ReferencesAll images provided by openclipart.orgAll video links provided by Khan Academy
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