Pre Algebra (Period 2 & 4)

Solving Multi-Step Equations 7-2


2 STEP EQUATIONS WITH SOME MORE STEPS BEFORE BALANCING



1) Sometimes equations have LIKE TERMS on the SAME SIDE.


The easiest first step is to COMBINE these before starting to balance:


9x -2x = -42
combine like terms ( those terms on the same side of the = sign)
7x = -42
now divide by 7
7x/7 = -42/7
x= -6


4a + 1 - a = 19

ADD THE 4a to the -1a FIRST

3a + 1 = 19


NOW SOLVE AS A 2 STEP EQUATION
3a + 1 = 19
-1 = -1
3a = 18
then
3a/3 = 18/3

a = 6



2) Sometimes equations have DISTRIBUTIVE PROPERTY on one side:

Usually, you want to do DISTRIBUTE FIRST!


UNLESS THE FACTOR OUTSIDE THE ( ) CAN BE DIVIDED
OUT OF BOTH SIDES PERFECTLY!!!!
(meaning it's compatible!)
In the following example you must distribute -2(2y + 8)


EXAMPLE: 
5y - 2(2y + 8) = 16

5y - 4y - 16 = 16 [distribute]

y - 16 = 16 [collect like terms]

y = 32 [solve by adding 16 to both sides]



But, with the following example you can divide both sides by 3 BEFORE you distribute
EXAMPLE:
3(4 + x) = 9

4 + x = 3 [Don't distribute! Divide both sides by 3.
The 3 goes into both sides perfectly!

x = -1 [Subtract 4 from both sides]

38 = -3(4y +2) + y
38 = -12y + -6 + y
38 = -11y - 6
+6 +6
44 = -11y
so then
44/-11 = -11y/-11


-4 = y

Useful Steps for Solving A Multi-Step Equation

Step 1: Use DP if necessary
Step 2: Combine like terms
Step 3: Undo Addition or subtraction using +prop= or -props=
Step 4: Undo Multiplication or division using xprop+ or ÷prop=