Solving Simple Inequalities 1-5 Solving Simple Inequalities Pre-Algebra Warm Up Solve. 1. x + 6 = 13 2. 8n = 48 3. t  2 = 56 4. 6 = x = 7 n = 6 t = 58 z 6 z = 36 Homework out to check!

Learn to solve and graph inequalities.

An inequality compares two quantities and typically uses one of these symbols:  < is less than is greater than   is less than or equal to is greater than or equal to

Additional Example 1: Completing an Inequality Compare. Write < or >. A. 23 – 14 6 9 6 > B. 5(12) 70 60 70 <

Try This: Example 1 Compare. Write < or >. A. 19 – 3 17 16 17 < B. 4(15) 50 60 50 >

An inequality that contains a variable is an algebraic inequality. A number that makes an inequality true is a solution of the inequality. The set of all solutions is called the solution set. The solution set can be shown by graphing it on a number line.

Word Phrase Sample Solutions Inequality Sample Solutions Solution Set x is less than 5 x < 5 x = 4 4 < 5 x = 2.1 2.1 < 5 1 2 3 4 5 6 7

Word Phrase Sample Solutions Inequality Sample Solutions Solution Set y is less than or equal to 2 y is at most 2 y  2 y = 0 0  2 y = 1.5 1.5  2 –3 –2 –1 0 1 2 3

Solving inequalities is the same as solving an equation, but with 1 exception – when you multiply or divide by a negative #.

Joke of the day A new teacher was trying to make use of her psychology courses. She started her class by saying, "Everyone who thinks you're stupid, stand up!“   After a few seconds, Little Johnny stood up.  The teacher said, "Do you think you're stupid, Little Johnny?"  "No, ma'am, but I hate to see you standing there all by yourself!"

Solve and graph the inequality. A. x + 2.5  8 –2.5 –2.5 Subtract 2.5 from both sides. x  5.5 1 2 3 4 5 6 7

Solve and graph the inequality. B. 5t > 15 5t > 15 Divide both sides by 5. 5 5 t > 3 1 2 3 4 5 6 7

Solve and graph the inequality. C. w – 1 < 8 + 1 + 1 Add 1 to both sides. w < 9 –3 0 3 6 9 12 15

Solve and graph the inequality. 4 D. 3  3  p 4 4 • 4 • Multiply both sides by 4. 12  p 0 3 6 9 12 15 18

Lesson Quiz Use < or > to compare each inequality. 1. 13 5(2) 2. 14 – 2 11 Solve and graph each inequality. 3. k + 9 < 12 4. 3  5. A school bus can hold 64 passengers. Three classes would like to use the bus for a field trip. Each class has 21 students. Write and solve an inequality to determine whether all three classes will fit on the bus. > > k< 3 –5 –4–3–2–1 0 1 2 3 4 5 m 2 6  m –4 –3–2–1 0 1 2 3 4 5 6 3(21)  64; 63  64; yes ?

Write an equation & solve Homework out Warm-up Write an equation & solve The average weight of an elephant is 5,450 kg. This is 4,270 kg more than the average weight of a giraffe. What is the average weight of the giraffe?

Positive choices Respect Integrity Determination Excellence P.R.I.D.E. Altadena Middle School P.R.I.D.E. P Positive choices R Respect I Integrity D Determination E Excellence Monday

Mid-chp 1 quiz You need 1 pieces of paper out