Algebra Period 3

REVIEW OF SIMPLE EQUATIONS 3-1 through 3-3

1 and 2-step equations
What is the goal? ... to determine the value of the variable
What does isolate the variable mean? ... getting the variable alone on one side of the equation
How? Use inverse operations ( the opposites) to 'get rid' of everything on the side with the variable.
FOCUS? ... on the variable
Addition/ Subtraction Properties of Equality
For all rational numbers a, b, and c if you begin with a= b then
a+c = b+c
as long as you add/subtract the same value to BOTH SIDES you are still equal or in balance
Sometimes, you combine these two properties becasue we say you never subtract-- you always ADD the Opposite

Multiplication/ DIvision Proeprties of Equality
For all rational numbers a, b, and c if you begin with a = b then
ac= bc
or a/c = b/c

Again, as long as you multiply/ divide the same valu to BOTH SIDES you are still equal or in balance

ALso works for (3/4) x = 12 because you multiply by the reciprocal....
You are using the Multiplication Property of Equality with the Multiplicative Inverse Property
that's 2 friends at once!!
(3/4)x = 12
(4/3)(3/4)x = 12 (4/3)
x = 16

Using both properties together 2-step equations

Use the Addition Property of Equality first ( get rid of addition or subtraction)
Use the Multiplication Property of Equality next ( get rid of mult/division)

Collecting Terms- sometimes you need to collect LIKE TERMS on the SMAE SIDE of the equation before balancing

FORMAL CHECK- 3 steps
1) REWRITE the original equation
2) SUBSTITUTE your solution and put a "?" over the equal sign
3) DO THE MATH and check it!!


2- Steps with distributive Property
USUALLY you want to distribut first!!
(Unless the factor outside the ( ) can be dividied out of BOTH SIDES PERFECTLY!!

5y -2(2y +8) = 16
5y -4y -16 = 16 {distibute accurately}
y - 16 = 16 { collect like terms}
y = 32 { solve by adding 16 to both sides!!}

-3(4 +3x) = -9
Wait you could distribute but if you divide both sides by -3
{the -3 goes into BOTH SIDES PERFECTLY}
you have 4 + 3x = 3
3x = -1 { subtract 4 from both sides}
x = -1/3 { Divide both sides by 3}

What if you have variables on BOTH SIDES of the equation?

Simplify each side of the equation first
THEN use the additive inverse property to move the variables to the other side, Usually we try to move the smaller coefficient to the larger because somethimes that avoids negative coefficients. But it isnot always the case.

3y - 10 - y = -10y + 12
combine like terms
2y - 10 = -10y +12
In this case I would add 10y to both sides to get rid of a negative coefficient
12y - 10 = 12
Now add 10 to both sides
12y = 22
Now divide both sides by 12
y = 22/12 or y = 11/6

Pre Algebra Period 2( Week of October 6)

Two Step Equations 7-1

Use the Addition Property of Equality or the Subtraction Property of Equality to get rid of addition or subtraction
+prop =
-prop =

Then use the Multiplication Property of Equality or the Division Property of Equality to get rid of multiplication or division
xprop =
÷prop=

This is the opposite of Aunt Sally because for solving equations you must work backwards-- or go in reverse!!

3x + 7 = 28
Subtract seven from both sides
-7 = -7 you subtract 7 form both sides so you used the -prop =
3x = 21
NOW Divide both sides by 3
3x/3 = 21/3
x = 7

CHECKING a 2 step equation

You need 3 steps to check also

1) rewrite the equation
3x + 7 = 28
2) substitute your answers and put a "?" over the "="
3) DO THE MATH!! use order of operations
3(7) + 7 ? 28
21 + 7 ? 28
28 = 28