 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:

  1 2 3 4 5 ( (3, ) 5. -1 0 1 2 3 4 5 6 7 [ ] 33) Y ≥ 0 [0, 5] 66) 2 ≥ |Y – a|

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

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|

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 ≈ 4.8584

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

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)  

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

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

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

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:

Ex) Ex)

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

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