Algebra Honors ( Periods 6 & 7)

Equations w/ The Variable on Both Sides 3-5

Partial Notes

6x = 4x +18
You can show the steps or if it is easy you can do them in your head... However, if you make too many errors, I will suggest that you actually show the balancing steps!
x = 9
Use the set notation
{9}

3y = 15 -2y
5y = 15
{3}

(4/5)x + 3 = x
This really becomes
3 = x( 1-4/5)
or 3 = (1/5)x
12= x
{15}

How do we do a formal check:
Step 1: Rewrite the original problem
Step 2: Substitute in the solutions
Step 3: REALLY do the MATH

(4/5)x + 3 = x
(4/5)(15) + 3 = 15
12 + 3 ?=? 15
15 = 15
Hooray!

(8+x)/9 = x
We talked about the various ways to do this...
I suggested using cross products
9x = 8 + x
or 8x = 8
{1}

7(a -2) - 6 =2a + 8 + a
7a - 14 - 6 = 2a + 8 + a
combine like terms on each side FIRST
7a - 20 = 3a + 8
4a = 28
a = 7
{7}



2 unique types of equations:
Identity equation: You solve it and you get the same thing on both sides...if you solve until you cannot do anything more, you get 0 = 0.
What this means is that you can pick any number and the equation will work!
The Distributive Property is the simplest example of an Identity Equation:
3(x + 7) = 3x + 21
Distribute on the left side and you'll get:
3x + 21 = 3x + 21
At this point, you should already know this is an Identity!
If you keep solving, you would subtract 3x from each side and you'll get:
21 = 21
and you know again that this is an Identity.
If you now subtract 21 from each side:
0 = 0
BUT I WOULDN'T GO THIS FAR! AS SOON AS YOU HAVE THE SAME THING ON BOTH SIDES, YOU CAN STOP AND SAY IT'S AN IDENTITY EQUATION!!!

Null set equation:
You solve it and you get an impossible answer:
3(x + 7) = 3x + 10
3x + 21 = 3x + 10
21 = 10
WHEN WILL THAT HAPPEN??? NEVER!!! SO THERE IS NO POSSIBLE SOLUTION TO THIS! The answer is the null set.