1. Notes P.3 – Linear Equations and Inequalities

2. I. Properties of Equality:
Let u, v, w, and z be real numbers, variables, or algebraic expressions
1. Reflexive
u = u
2. Symmetric
If u = v, then v = u
3. Transitive
If u = v & v=w, then u = w
4. Addition
If u = v & w=z, then u + w = v + z
5. Multiplication
If u = v & w=z, then uw = vz

3. II. Confirming Solutions
A. Substitution – NEVER PLUGGING IT IN !!!!
B. Graphically

4. III. Solving ax +b = c
A. By Hand – Isolate the variable and coefficent
B. By TI-83+/84
1.) Y1 = ax+b
2.) Y2 = c
3.) GRAPH – 2nd CALC – INTERSECT – ENTER – ENTER - ENTER

5. IV. Properties of Inequalities:
Let u, v, w, and z be real numbers, variables, or algebraic expressions
1. Transitive
If u < v & v < w, then u < w
2. Addition
If u < v, then u + w < v + w
If u < v & w < z, then u + w < v + z
3. Multiplication
If u < v, & c > 0then uc< vc
If u < v, & c < 0then uc> vc

6. V. Solving Linear Inequalities
A. By Hand – Same as III
B. By TI-83+/84 – Same as III

7. VI. Solving Double Inequalities
A. Work both simultaneously!
B. Example -

8. VII. Quick Review
Complete the in-class worksheet.

9. Homework: p. 25 #3,7,23,27,33,41,45,49,53,57,63-68,70-73