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. Reflexiveu = u 2. SymmetricIf u = v, then v = u 3. TransitiveIf u = v & v=w, then u = w 4. AdditionIf u = v & w=z, then u + w = v + z 5. MultiplicationIf 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.) Y 1 = ax+b 2.) Y 2 = c 3.) GRAPH – 2 nd CALC – INTERSECT – ENTER – ENTER - ENTER

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