Notes P.3 – Linear Equations and Inequalities

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

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

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

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

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

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

VII. Quick Review Complete the in-class worksheet.

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