Math 6 Honors ( Periods 1, 2, & 3)

Solving Other Equations & Inequalities 2-5



Before we began today's lesson, we reviewed some of the difficult mathematical expressions and equations found on Page 448. We discussed the importance of a well placed comma... in MATH as well as in Language Arts!!

Our math example was
the sum of three and a number b, times even
(3 + b)7

and
the sum of three and a number b times seven
3 + 7b

Our Language Arts example... is one of my favorites.

Where does the comma belong in the following:
A woman without her man is nothing.

I insist it is...
A woman, without her, man is nothing.
However, I acknowledge that some men would differ and insist it is
A woman, without her man, is nothing.
So you see, the comma makes all the difference... in math expressions and equations as well as in language arts!!

We solve by "undoing" the operations in each equation.

We use inverse operation & undo Aunt Sally
It's the reverse of PEMDAS!!


GOAL: You use the INVERSE operation to ISOLATE the variable on one side of the equation


GOLDEN RULE OF MATHEMATICS
What you do to one side of the equation you MUST do to the other side!!

GOAL: You use the INVERSE operation to ISOLATE the variable on one side of the equation


Here are the steps and justifications (reasons)

1. focus on the side where the variable is and focus specifically on what is in the way of the variable being by itself ( isolated)

2. What is the operation the variable is doing with that number in its way?

3. Get rid of that number by using the opposite (inverse) operation

*Use + if there is a subtraction problem
*Use - if there is an addition problem
*Use x if there is a division problem
*Use ÷ if there is a multiplication problem

GOLDEN RULE OF EQUATIONS; DO UNTO ONE SIDE OF THE EQUATION WHATEVER YOU DO TO THE OTHER!!

4. Justification: You have just used one of the PROPERTIES OF EQUALITY
which one?

that's easy-- Whatever operation YOU USED to balance both sides that's the property of equality
We used:

" +prop= " to represent Addition Property of Equality
" -prop= " to represent Subtraction Property of Equality
" xprop= " to represent Multiplication Property of Equality
" ÷prop= " to represent Division Property of Equality

5. You should now have the variable all alone (isolated) on one side of the equal sign.

6. Justification: Why is the variable alone?
For + and - equations you used the Identity Property of Addition (ID+) which simply means that you don't bring down the ZERO because you add zero to anything-- it doesn't change anything... [Note: there is no ID of subtraction]

For x and ÷ equations, you used the Identity Property of Multiplication (IDx) which simply means that you don't bring down the ONE because when you multiply by one it doesn't change anything [NOTE: there is no ID of division]

7. Put answer in the final form of x = ____and box this in.