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Solving Equations (Multiplication & Division)

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

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Solving Equations (Multiplication & Division)

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

  2. 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

  3. 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

  4. 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.

  5. 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.

  6. 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.

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

  8. 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?

  9. 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.

  10. 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

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

  12. 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.

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

  14. 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?

  15. Solving Algebraic Expressions • Take extra careful note: • (6)(6) = 36 • (-6)(6) = -36 • (6)(–6) = -36 • (-6)(-6) = 36

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