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Solving Equations: a strategy

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The mathematics behind solving equations is basic. The hardest part: What do I do first?…

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THE GREAT SOLVING EQUATIONS PLAN!!! The following plan will allow you to solve any equation you come across in five easy steps…

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Step 1: Eliminate any denominators using the LCD technique.

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Step 2: Eliminate any brackets using the Distributive Law. Brackets lock terms together……that’s bad!

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Step 3: Collect like terms on each side of the equation. Remember the sign in front of the term stays with the term.

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Step 4: Isolate the variable. Eliminate the smaller variable if they are on both sides.

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Step 5: Solve the 2 step equation. Add/sub first, then mult/divide.

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Solve the following equations: 1. 4x = 20 44 1 1 x = 5

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2. 7 + 3y = 34 33 1 1 y = 9 -7 3y = 27 Check this answer

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Check 7 + 3(9) = 34 ? 7 + 27 = 34 34 = 34 YES!!!

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3. 3z + 4 = 8z - 21 -5 1 1 -5z = - 25 -8z -5z + 4 = -21 -4 z = 5 Check this answer

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Check 3(5) + 4 = 8(5) – 21 ? 15 + 4 = 40 – 21 ? 19 = 19 YES!!!

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4. 2(x + 3) = 10 22 1 1 x = 2 -6 2x = 4 2x + 6 = 10 Check this answer

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Check 2(2 + 3) = 10 ? 2(5) = 10 10 = 10 YES!!!

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5. 3 + 4(x – 2) = 6x + 7 – 1x 1 1 -1x = 12 -5x -1x – 5 = +7 4x - 5 = 5x + 7 3 + 4x – 8 = 6x + 7 – 1x +5 x = - 12

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6. 4 3 d=12 4 3 d = 12 X 3 3 X 1 1 4d = 36 4 4 1 1 d = 9

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Homework Re-attempt various problems.

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