Bell Ringer Represent to following in a compound

Bell Ringer Represent to following in a compound inequality: 1. You must spent more than $5 but less than $30 to receive the sale price. 2. You need to buy shirts for the AC. You need to buy at least 10 for the company to take your order, but you cannot exceed 145.

Compound Inequalities • SWBAT solve and graph a compound inequality

Compound Inequality A compound inequality consists of two inequalities connected by and or or.

What is the difference between and or? A B AND means intersection -what do the two items have in common? OR means union -if it is in one item, it is in the solution

1) Graph x < 4 x ≥ 2 a) Graph x < 4 o 2 3 4 b) Graph x ≥ 2 ● 2 c) Combine the graphs d) Where do they intersect? ● 2 3 o 4

2) Graph x < 2 or x ≥ 4 a) Graph x < 2 o 2 b) Graph x ≥ 4 2 3 3 c) Combine the graphs 4 ● 4

Steps for Solving Compound Inequalities 1. 2. 3. 4. 5. Determine if the inequality is an “and” or and “or” type. Separate the compound inequality into 2 pieces and solve both. Graph each result on the same number line Pay attention to your boundaries. GOAL: Get variable by itself in the middle

Bell Ringer Graph the following compound inequalities on the number line. v -2 < x <5 v v x < 4 or x ≥ 0

There is no bell ringer today v Please sit quietly and wait for instructions

Solving Compound Inequalities Example: Separate Now solve

Solving Compound Inequalities

Solving Compound Inequalities You try…watch the trap…. . with negatives

Your Turn X is less than 4 and is at least -9

Solve:

Solve

Solve 'A cookie contains 9 grams of fat. If you eat no fewer than 4 and no more than 7 cookies, how many grams of fat will you consume? '

Introduction to Absolute Value

What are opposites on a number line? Graph the integer set from – 5 to + 5 Two numbers that are the same distance from zero are said to be opposites

But what is Absolute Value? Absolute Value is the distance a number is from zero. Remember distance itself is ALWAYS positive

How do we denote absolute value? SO let’s try a few: What general statement can you make about absolute value?

Be careful! In math a negative sign in front of the absolute value sign should be read “take the opposite of”. This means treat the absolute value sign like a grouping symbol. Do the work inside first THEN take the opposite of

Let’s try a few