Basic
Algebra  Lesson 6
Balancing Equations
to Solve Variables
by
Elaine Ernst Schneider
Objective(s):
By the end of this lesson the student will be able to:
balance equations to solve
for variables (solve for 'x') 
Pre Class
Assignment: Completion or review
of Basic Algebra  Lesson
5
Resources/Equipment/Time
Required:
Outline:
In the last lesson, you learned to
write expressions and to find the values of expressions.
When two expressions can be written
to balance or equal one another, it is called an
equation. In other words, whatever
is expressed on one side of the equal sign is calculated to be the exact
same value as whatever is on the other side of the equal sign. IN other
words, the left member and the right member of the equation "balance."
Examples of equations:
5 + 7  2 = 2(5) (the answer
on the left side is 10 and the answer on the right side is 10)
100/25 = 347  343 (the answer
is 4 on the left of the equal sign and 4 on the right also)
Equations involving unknown variables
are solved by balancing the left member and the right member. For example,
in the equation y + 5 = 12, I know that the left member must equal 12 for
it to balance with the right member. This means y would be 7 because 7
+ 5 = 12. That one is easy enough to do the math without a formal procedure.
But because algebraic equations can become much longer and more calculated,
a system is necessary to solve for variable and balance equations.
Let's take the above equation:
y + 5 = 12
The proper procedure in solving for
y is to "isolate" y. This means we want y to stand by itself on one
side of the equal sign.
Now, keep in mind that we want every
thing to "balance" on either side of the equal sign. This means whatever
I do to the left member, I must do to the right member. So, to isolate
y and solve the equation, I must "move" the 5 to the other side of the
equal sign. To do this, I must make it zero on the left side of the equation
by subtracting 5:
y + 5 = 12
y + 5  5 = 12  5
y + 0 = 12  5
y = 7
Try solving for the variable by keeping
each side equal. Remember, the idea is to "balance" the equation, so what
you do to one side, you must do to the other.
100/5 = y + 2
100/5 2 = y +2  2
20  2 = y
18 = y **
**The answer
displayed prior to June 10/01 was incorrect and unreported. Thanks to the
class of L. Crawford for the notice. JM
Now it's time for you to try a few...
Assignment(s)
including Answer key:
EXERCISE:
1. y  10 = 17
2. c + 4 = 29
3. 5y = 90
4. 1/3 t = 29
5. 6y = 72
6. 1/9 g = 58
7. 4y = 100
8. 12a = 132
9. r + 9 = 48
10. x + 79 = 422
Cut Here 
ANSWER KEY:
1. 27
2. 25
3. 18
4. 87
5. 12
6. 522
7. 25
8. 11
9. 39
10. 343
PreRequisite
To: Basic Algebra
Lesson 7
