Pre Algebra (Period 2 & 4)

Solving Two-Step Equations 7-1
TWO STEP EQUATIONS:

1. Use the ADDITION PROPERTY OF EQUALITY (first) 
(get rid of addition or subtraction)

Addition property of equality abbreviated as +prop=

Subtraction property of equality abbreviated as -prop=


2. Use the MULTIPLICATION PROPERTY OF EQUALITY (second) 
(get rid of multiplication/division)

Multiplication property of equality abbreviated as ×prop=
Division property of equality abbreviated as ÷ prop=

DID YOU NOTICE THAT THIS IS THE OPPOSITE OF AUNT SALLY?


That's because solving equations is actually doing order of operations backwards!



EXAMPLE:

3x + 7 = 28
         
-7  -7     

SUBTRACT 7 FROM BOTH SIDES

3x = 21

NOW DIVIDE BOTH SIDES BY 3


3x = 21

3     3



x = 7


CHECKING A 2 STEP EQUATION:

You'll need 2 steps to check, too!

(1) Re write the equation

3x + 7 = 28

(2) SUBSTITUTE YOUR ANSWER AND PUT A ? OVER THE =



3(7) + 7 = 28

USE ORDER OF OPERATIONS - MULTIPLY FIRST

(3) Do the Math!! Really do the Math!!
21 + 7 = 28

28 = 28


-d/7 + 21 = 0

(okay addition or subtraction first so... since + 21 O will need to subtract 21_
-d/7 + 21 = 0
-21 -21
-d/7 + 0 = -21

-d/7 = -21
Now since it is minus d divided by 7 I need to multiply both sides by 7
but if I only use 7 I will still have a negative d and I want to end up with just d... so what if we multiply both sides by -7

(-7)(-d/7) = -21(-7)
d = 147

9 - 3p = -27
most students think that the - sign is attached to the 0 but IT IS NOT!!
this is 9 minus 3p so
9- 3p = -27
you need to subtract 0 from both sides to clear the +9 in the original equation
9 -3p = -27
-9 -9
-3p = -36

Wait how did I get -36... well we have -27 - 9 on the right side and using the integer rules... same sign rule... just add them and use their sign...

now
-3p = -36
If I divide both sides by 3 I still would have a negative on the left with the variable so I must divide both sides by -3
-3p = -36
-3 -3

p = 12