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 SolutionsA. Substitution – NEVER PLUGGING IT IN !!!!

B. Graphically

III. Solving ax +b = cA. 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 InequalitiesA. By Hand – Same as III

B. By TI-83+/84 – Same as III

VI. Solving Double InequalitiesA. Work both simultaneously!

B. Example - 1 3 7 8x

6 3 15x

2 5x

[2,5)

VII. Quick ReviewComplete the in-class worksheet.