Download Lecture Notes for Section 2.2

Elementary Algebra Notes
Section 2.2
Page 1 of 2
Section 2.2: The Multiplication Property of Equality
Big Idea:
 To solve an equation, you must do the opposite of the order of operations. To solve an equation, you
want to isolate the variable using the following steps:
o Simplify both sides, if possible, by using the distributive property or by combining like terms.
o Use the Addition Property of Equality to add or subtract a number (or variable term) from both
sides so that the variable begins to be isolated.
o Use the Multiplication Property of Equality to multiply (or divide) both sides of the equation by
a number so that the variable gets more isolated.
Big Skill: You should be able to solve slightly more complicated equations using the addition and
multiplication properties of equality, and then check your solution.
The multiplication property of equality: You can multiply (or divide) each side of an equation by the same
NONZERO number without changing the solution. Algebraic statement:
If
A = B,
then AC = BC
are equivalent equations as long as C  0.
Practice: Solve the following equations, then check your work.
x
8
1.
2
2. 3x  21
3. 7 x  12
4.  x  156
5.
4
x  16
3
Algebra is:
the study of how to perform multi-step arithmetic calculations more efficiently,
and the study of how to find the correct number to put into a multi-step calculation to get a desired answer.
Elementary Algebra Notes
Section 2.2
Page 2 of 2
9
27
6.  x 
2
4
7. 22.7 x  265
8. 12t  7  3t  9  20
9. 8t 10 10t  9  2  2t  3
10. 3  y  7   24
11.
2
1
1
x x
x  18
5
10
20
12. Use our expression for the cost of golf clubs to find out how many games you can play if you only have
$500 to spend on golf.
13. Suppose you are planning a wedding, and the reception hall costs a flat fee of $500 plus $15 per guest
for food and $30 per guest for open bar. All of this has tax added on. If you have $2,000 to spend on
the reception, how many guests can you invite?
Algebra is:
the study of how to perform multi-step arithmetic calculations more efficiently,
and the study of how to find the correct number to put into a multi-step calculation to get a desired answer.