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Its a party! Solving Multi-step Equations A GEMS Submission for ALEX Submitted by: E. Thompson, PhD. Summer 08

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Review of One-Step Equations 2x = 8 x +3 = 15 x – 5 = 20 Be sure you can solve each type of problem before we begin!

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With Multi-Step Equations it can be hard to know where to start…. pretend its a party! You are the host - a.k.a. X In what order do people leave a party? – Enemies (get rid of them to avoid trouble) – Acquaintances (after mingling with everyone, they usually leave early) – Friends (they hang out with the host a little longer) – Family (if attending, they will stay to the end to help clean)

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Who is who? Consider our one-step equations 2x = 8 x +3 = 15 x – 5 = 20 FAMILY….right beside you…and only you… until the end! FRIENDS….they are close to you…they stay longer than some people, but not as long as family

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Who are the acquaintances? ACQUAINTANCE ACQUAINTANCE – Because this number mingles with all other many parts of the equation instead of giving most of its attention to the host (x), it is not a friend…it is an acquaintance.

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Identify all the Party-goers ACQUAINTANCE FRIEND FAMILY

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The equal sign is the door…who goes out the door first? ACQUAINTANCE – multiply each side of the equation by 3. The work: The result: We still have company... lets continue….

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Who is next to leave? Friends – add 5 to each side. The work: The result: All that is left is family…a familiar one-step equation.

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Clean up the party with a family member Family – divide each side by 2 The work: The result: Dont forget to check your work with Order of Operations!

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Try these problems: Try these problems: Steps: 1.Identify the party-goers 2.Eliminate party-goers in order 3.Get x (the host) alone 4.Check your solution

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Enemies can ruin the entire party…get rid of them first! Its easy to spot an enemy…they affect everything! To solve, multiply each side by the reciprocal The work: The result: Try to complete the problem from here….the answer is: 21

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Its party time! Do you know who is in your home? Enemy Acquaintanc e Friend Family HOST The Door! See if you can ID the enemy, the friend, the acquaintance, a family member, the host and the door!

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The more you party, the more responsible you will become! l TIPS: – Enemies and acquaintances are very similar…both affect the entire equation. Typically there are only enemies when you have already identified an acquaintance. – Eventually, you will partiers outside the door (operations on both sides of the equal sign). Start these by using the same method to get everyone on one side.. – If you find yourself (the host) in two places at once (variables on both sides of the equal sign), use the same method to regroup yourself back into the house.

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