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

Solving Equations & Inequalities 2-4


To solve equations you need to ISOLATE the variable on one side of the mathematical sentence.
isolate--> means to get the variable alone on one side of the equal sign or the inequality sign.


Properties of Equality:
Property of Equality allows us to add or subtract the same number from BOTH sides of the equation.

Addition Property of Equality abbreviated as +prop=
Subtraction Property of Equality ( written as -prop= )



Identity Property of Addition ( our textbook calls it the Addition Property of Zero)
We abbreviated it as ID(+) a + 0 = a

Remember to JUSTIFY with the properties

We completed a yellow form-- see tonight's homework assignment if you need to print it out. That sheet gets glued into our spiral notebook


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.