Math 6H (Period 6 & 7)

Solving Equations & Inequalities 2-4

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

Its exactly like unwrapping a present... which I did in class today!! :)

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


w + 18 = 64 we must undo addition using the inverse of + (that is, subtraction)
- 18 -18
w + 0 = 46
and then we write
w = 46


What property allows us to subtract 18 from both sides of the equation?
The SUBTRACTION property of equality which we abbreviate with
-prop=

What property allows us to write w instead of w + 0
w + 0 = w
That is the Identity Property of Addition.

How about
p - 84 = 102 we must undo subtraction using the inverse of - (which is ADDITION)

p - 84 = 102
+84 +84
p + 0 = 186
and then we write
p = 186

What property allows us to add 84 to both sides of the equation?
the addition property of equality, which we abbreviate as
+prop=

What property allows us to write p instead of p + 0
The Identity property of Addition.
Why is it called the Identity Property of Addition?
The number never changes its identity
a + 0 = a for all numbers!!

What happens if we have
b + 7 > 8
This is an inequality but we solve this as we would an equation

b + 7 > 8
- 7 -7
b + 0 > 1
and then we write b > 1

h - 7 > 7
+ 7 +7
h + 0 > 14
and then we write
h > 14

Our textbook gives the answer as "greater than 14" but I want you to put it in math symbols. That is, please answer with
h > 14.