Transcript Solving Equations (Addition & Subtraction)

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;
► x + 6 – 6 = 36 – 6 ; we eliminate +6 by
subtracting 6 (the opposite of the
operation).
► x = 30
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
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.
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.
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.
Solving Algebraic Expressions
► Example
# 3: Solve for g, if 9g = 54
► Try this one on your own!
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?
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.
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
Solving Algebraic Expressions
► Since
2/2 = 1;
► h = 20
► Don’t forget to check your answer.
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.
Solving Algebraic Expressions
► Example:
Solve for k, if k = 12
►
5
► Try this one on your own!
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?
Solving Algebraic Expressions
► Take
extra careful note:
► (6)(6) = 36
► (-6)(6) = -36
► (6)(–6) = -36
► (-6)(-6) = 36