1.  Warm-up: n HW: Pg. 10 (40) Pg. 12 (75, 79, 84, 85, 8996, 110) n
HW:
Pg. 10 (40)
Pg. 12 (75, 79, 84, 85, 8996, 110)
Simplify:

2. (
(3, ) 5. [ ]
33) Y ≥ 0
[0, 5]
66) 2 ≥ |Y – a|

3. P.1: Real Numbers Objective: Evaluate absolute values
Know the basic rules of algebra
Evaluate algebraic expressions
Use the basic rules and properties of algebra

4. Absolute Value Properties
If a, b, and c, are any real numbers, then
Property 5 |– a| = |a|
Property 6 |ab| = |a| |b|
Property 7 (b ≠ 0)
Property 8 |a + b| ≤ |a| + |b|

5. Examples Evaluate the expression |p – 5| + 3 Solution
Since p – 5 < 0, we see that
|p – 5| = –(p – 5).
Therefore
|p – 5| + 3 = – (p – 5) +3
= 8 – p ≈

6. Examples Evaluate the expression Solution Since , we see that
Similarly, , so
Therefore,

7. Algebraic Expressions
 An algebraic expression is a collection of letters (variables) and real numbers (constants) combined using math operations
Ex) 3x2 + 5x - 7
Variable terms
Constant term
Coefficeints
Terms and Coefficients
3x2 + 5x + (- 7)

8. Ex) Evaluate each expression for each value of x
Ex) Evaluate each expression for each value of x. If not possible state the reason.

9. Definition of Subtraction: Add the opposite.
a – b = a + (-b)
Ex) 12 – 27
Definition of Division: Multiply by the reciprocal.
Ex)

11. Properties of Negation and Inequality:
(-1)a = -a
-(-a) = a
(-a)b = -(ab) = a(-b)
(-a)(-b) = ab
-(a + b) = (-a) + (-b)

12. Properties and Operations of Fractions:
Equivalent Fractions: ad = bc
Rules of Signs:
Generate Equivalent Fractions:
Add or Subtract with Like Denominators:
Add or Subtract with Unlike Denominators:
Multiply Fractions:
Divide Fractions:

13. Ex)
Ex)

14. Properties of Equality
Let a, b, and c be real numbers, variables, or algebraic expressions.
If a = b, then a + c = b + c
If a = b, then ac = bc
If a + c = b + c, then a = b
If ac = bc, then a = b

15. Sneedlegrit: Simplify
Homework:
Pg. 10 (40)
Pg. 12 (75, 79, 84, 85, 8996, 110)
Simplify:
Sneedlegrit: Simplify