Compound Inequalities CA 5.0

Objective - To solve compound inequalities involving “and”.

ABSOLUTE VALUE INEQUALITIES  ALWAYS isolate the absolute value FIRST!  NEVER distribute into absolute value!  Absolute value equations usually have 2 answers! │stuff│= pos 2 solutions │stuff│= 0 1 solution │stuff│= neg no solution  FORM: Variable / Symbol / Number  When multiplying or dividing by a negative number you MUST flip the inequality symbol!  Less th“and” “and” where things overlap  Great“or” “or” everything together symbol > < ≥ ≤ arrows ABSOLUTE VALUE INEQUALITIES

Curriculum Vocabulary Compound Inequality: An inequality the is formed by the union ∪ (“or”) or the intersection ∩ (“and”) of two simple inequalities. Conjunction:   Disjunction:  

N.B. The numbers MUST be written in order, as on a number line! Write a compound inequality that describes all the real numbers greater than -2 and less than 5. and “In-between statement” N.B. The numbers MUST be written in order, as on a number line! -3 -2 -1 0 1 2 3 4 5 6

Write the following compound inequalities as “In Between” statements. 1) 2) 3)

Solve and graph the compound inequality. -7 0 4

Solve and graph. -3 0 1

Solve and graph. -2 0 10

A racquetball club charges a $20 membership and $2 per hour. How many hours per month can be played on a budget of $50 to $70? Let x = # of hours C = total cost C = 20 + 2x You can play from 15 to 25 hours per month