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Solving Equations (Multiplication & Division) Grade Seven & Eight Mathematics M. M. Couturier

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Solving Algebraic Expressions ► Recall that when solving problems of this nature: ► x + 6 = 36; when isolate the x by eliminating what is next to it; ► x + 6 – 6 = 36 – 6 ; we eliminate +6 by subtracting 6 (the opposite of the operation). ► x = 30

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Solving Algebraic Expressions ► Likewise, if the problem were, ► x - 6 = 36; we would still isolate the x but this time we add 6 (the opposite of –6) ► x - 6 + 6 = 36 + 6 ; which yields; ► x = 42

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Solving Algebraic Expressions ► When faced with a multiplication problem, we will use a similar strategy; ► Example: ► 3x = 15 ► First we want to isolate x; but to do so we must eliminate the multiple of 3. To do so, we will have to divide both sides by 3.

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Solving Algebraic Expressions ► This means we will have: ► 3x = 15 ► 3 3 ► Since 3/3 = 1, the x is isolated; ► x = 5; ► Don’t forget to do your check.

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Solving Algebraic Expressions ► Example # 2: Solve for f, if 6f = 66 ► First we will want to isolate for f, so we are going to have to divide both sides by 6. ► 6f = 66 ► 6 6 ► Since 6/6 = 1, f is isolated; ► f = 11; ► Don’t forget to do your check.

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Solving Algebraic Expressions ► Example # 3: Solve for g, if 9g = 54 ► Try this one on your own!

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Solving Algebraic Expressions ► Solution to Example # 3: Solve for g, if 9g = 54 ► First step: isolate for g; by dividing both sides by 9. ► 9g = 54 ► 9 9 ► Since 9/9 = 1, g is isolated; ► g = 6; ► Did you do your check?

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Solving Algebraic Expressions ► What about division problems? Well, what is the opposite of division; multiplication! So when faced with a division problem, you will isolate the variable in question by multiplying both sides by its denominator.

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Solving Algebraic Expressions ► Example: Solve for h; h = 10 ► 2 ► Our first step is to isolate the h, so to do that we must eliminate the ½. To do that, we will multiply both sides by 2. ► (2)h = 10(2) ► 2

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Solving Algebraic Expressions ► Since 2/2 = 1; ► h = 20 ► Don’t forget to check your answer.

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Solving Algebraic Expressions ► Example: Solve for p, if p = 7 ► 3 ► Isolate p by multiplying 3 on both sides. ► p = 7; ► 3 ► (3)p = 7(3) ► 3 ► Since 3/3 = 1; ► p = 21 ► Don’t forget to check your answer.

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Solving Algebraic Expressions ► Example: Solve for k, if k = 12 ► 5 ► Try this one on your own!

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Solving Algebraic Expressions ► Example: Solve for k, if k = 12 ► 5 ► Isolate k by multiplying 5 on both sides. ► k = 12; ► 5 ► (5)k = 12(5) ► 5 ► Since 5/5 = 1; ► p = 60 ► Did you check your answer?

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Solving Algebraic Expressions ► Take extra careful note: ► (6)(6) = 36 ► (-6)(6) = -36 ► (6)(–6) = -36 ► (-6)(-6) = 36

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