Bell Work Write an inequality Solve it The World Travelers Club is selling chips to raise money to go to Australia.  It costs $4500 in total.  Ulises receives $300 from a rich old man as a donation. If he charges $1.50 for each bag of chips, how many does he need to sell in order to raise at least enough for his trip? Write an inequality Solve it

Bell Work What is this a picture of?

Bell Work THE SHOWDOWN Get in your groups of 4 1 Showdown Captain 3 students with whiteboards

Compound inequalities A compound inequality are two inequalities connected by the words “and” or “or”. For example: 2 < x < 6 2 3 1 4 5 6 7 8 9

At the Golden Corral, an individual must be between 3 years AND 12 years old to pay the child's price.   3 12

In order to get a flu shot for free you have to be less than or equal to 5 years old OR 65 years or older. 5 65  

Graphing “AND” 0 < x < 4 -1 -2 1 2 3 4 5 6 -2 1 2 3 4 5 6 “AND” cases have the variable in-between two numbers. The graph is in-between two numbers.

Graphing “OR” x < -1 or x > 2 -1 -2 1 2 3 4 5 6 -2 1 2 3 4 5 6 x < -1 or x > 2 OR cases have TWO separate answers and are solved (and graphed) separately (but on the same number line).

AND or OR

Solving “AND” SOLVE: Isolate the variable in-between the inequality symbols. IMPORTANT – opposite operations apply to the WHOLE THING (that means both sides!). -2 <x – 8 < 10 Original Problem -2 + 8 < x – 8 + 8 < 10 + 8 Add 8 6 < x < 18 Simplify

Solve 4 < x – 5 < 12. Graph the solution. I DO Solve 4 < x – 5 < 12. Graph the solution.

Solve -9 < 3x + 6 < 10. Graph the solution. YOU TRY! Solve -9 < 3x + 6 < 10. Graph the solution.

Solving “OR” 3x + 1 < 7 OR 11x – 4 > 62 SOLVE: You MUST solve AND graph each inequality separately (but on the same number line). Solve: 3x + 1 < 7 OR 11x – 4 > 62

Solve Separately, Graph Together YOU TRY! Solve Separately, Graph Together 3 + p >14 OR -2p + 6 > 30

Multiplying or Dividing by negative numbers AND Inequality Reverse BOTH signs -2 < -x < 5 2 > x > -5

only reverse it if it applies to the individual inequality. Multiplying or Dividing by negative numbers “OR” inequalities only reverse it if it applies to the individual inequality. -3x + 1 < 7 OR 11x – 4 > 62

YOU TRY! Solve -2 < -2 – x < 1

Compound Inequalities When graphing compound inequalities, be sure that the graph satisfies BOTH if it is AND or ONE if it is OR…….inequality. -3 > x OR x > 2 -4 -3 -5 -2 -1 1 2 3

Write an inequality that describes each condition. a. Water is a nonliquid when the temperature is 32 degrees F or below, or is at least 212 degrees F. b. A refrigerator is designed to work on an electric line carrying from 115 to 120 volts.

Quick Review Solve inequalities just as you would equations using inverse operations, KNOW WHEN AND WHEN NOT TO FLIP INEQUALITY SIGNS!!! Make sure your graph agrees with the inequalities involved. What does the graph of a compound inequality (AND) case look like? OR Case?

Homework P208, 16-26 even, 30-34 even, 47-50