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Section 1.8Solving
Addition and Subtraction Equations
Which word do you think “Equation” has a connection
to?
YOU’RE CORRECT!
An equation is a
mathematical sentence
that contains an equal sign.
The part on the left side of the equal sign has the same value as the part on the right side. One or
both sides may contain a variable.
What is a variable?
A. A number that changes constantly.
B. A letter or symbol that stands for a number.
C. A number that varies as you move away from zero.
YOU’RE CORRECT!
A variable is a letter or
symbol that stands for a
number.
To solve an equation, you
must find what the variable
represents so that the two
parts are equal.
Equations are like balance scales. In order to keep a scale balanced you must have the same amount of weight on both sides.
If I took one block away from the left side, what would I have to do to keep
the scale from tipping?
If I added 6 more apples to the right side, how could I keep the scale from
tipping?
To keep an equation equal,
we must do exactly the same thing to each side
of the equation. If we add a number to one side, we
must add that same number to the other side
and vice versa.
Addition and subtraction are called “opposite
operations” because they can ‘undo’
each other.
What are the other two opposite
operations?
Multiplication and division are opposite operations,
too!
for Solving Addition and Subtraction Equations
1. Look to see what side the
variable is on.
2. Decide what
operation is being shown.
3. Do the opposite of
that operation to both sides.
4. Write what
number the variable
stands for (ex: a = 2).
5. Check the solution by “plugging” the number back into the equation to see if the sides are equal.
Example 1m + 18 = 34 Look for variable
-18 -18 Do the opposite
m = 16 Write what m is
m + 18 = 34
16 + 18 = 34 Plug in m
34 = 34 Solution is correct!
If you check your solution and you do
not come out with the same numbers, then your solution is not correct. Therefore,
you must rework the problem.
Always check your answers to equations.
It is the only way to make sure you get a
problem correct. Why miss a problem when
you can get all of them correct?
Example 2 68 = y + 43 Look for variable
-43 -43 Do the opposite
25 = y Write what y is
68 = y + 43
68 = 25 + 43 Plug in y
68 = 68 Solution is correct!
Example 3 t - 14 = 22 Look for variable
+ 14 +14 Do the opposite
t = 36 Write what t is
t - 14 = 22
36 - 14 = 22 Plug in t
22 = 22 Solution is correct!
Try These...1. r + 5 = 18
2. m - 26 = 59
3. 102 = x - 15
4. a + 39 = 56
r = 13
m = 85
117 = x
a = 17
Let’s do Checking for
Understanding Page 47 # 4 - 9
Prediction:You will show all of the
steps (including checking) as you have been shown today or
credit will not be given for your homework.
Are there any questions
about solving addition or subtraction equations?
Homework:
Page 48 12-34 even
Don’t forget to check your solution!