Solving Simple Inequalities 1-5 Solving Simple Inequalities Pre-Algebra Learn to solve and graph inequalities.

Solving Simple Inequalities 1-5 Solving Simple Inequalities Pre-Algebra 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

Solving Simple Inequalities 1-5 Solving Simple Inequalities Pre-Algebra Example 1: Completing an Inequality Compare. Write < or >. A. 23 – 14 6 9 6 > B. 5(12) 70 60 70 <

Solving Simple Inequalities 1-5 Solving Simple Inequalities Pre-Algebra Word Phrase 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

Solving Simple Inequalities 1-5 Solving Simple Inequalities Pre-Algebra Word Phrase Inequality Sample Solutions Solution Set a is greater than 0 a is more than 0 a > 0 a = 7 7 > 0 a = 25 25 > 0 –3 –2 –1 0 1 2 3

Solving Simple Inequalities 1-5 Solving Simple Inequalities Pre-Algebra Word Phrase 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 Simple Inequalities 1-5 Solving Simple Inequalities Pre-Algebra Word Phrase Inequality Sample Solutions Solution Set m is greater than or equal to 3 m is at least 3 m ≥ 3 m = 17 17 ≥ 3 m = 3 3 ≥ 3 –1 0 1 2 3 4 5

Solving Simple Inequalities 1-5 Solving Simple Inequalities Pre-Algebra Most inequalities can be solved the same way equations are solved. Use inverse operations on both sides of the inequality to isolate the variable. There are special rules when multiplying or dividing by a negative number, which you will learn in the next chapter.

Solving Simple Inequalities 1-5 Solving Simple Inequalities Pre-Algebra Example 2A: Solving and Graphing Inequalities 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 According to the graph, 5.4 is a solution, since 5.4 < 5.5, and 6 should not be solution because 6 > 5.5.

Solving Simple Inequalities 1-5 Solving Simple Inequalities Pre-Algebra Example 2B: Solving and Graphing Inequalities 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

Solving Simple Inequalities 1-5 Solving Simple Inequalities Pre-Algebra Example 2C: Solving and Graphing Inequalities 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

Solving Simple Inequalities 1-5 Solving Simple Inequalities Pre-Algebra Example 2D: Solving and Graphing Inequalities Solve and graph the inequality. p 4 D. 3 ≥ 3 ≥ p 4 4 • 4 • Multiply both sides by 4. 12 ≥ p 0 3 6 9 12 15 18

Solving Simple Inequalities 1-5 Solving Simple Inequalities Pre-Algebra 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

Solving Simple Inequalities 1-5 Solving Simple Inequalities Pre-Algebra Try This: Examples 2A and 2B Solve and graph each inequality. A. x + 2 ≥ 3.5 –2 –2 Subtract 2 from both sides. x ≥ 1.5 1 2 3 4 5 6 7 B. 6u > 72 6u > 72 Divide both sides by 6. 6 6 u > 12 3 6 9 12 15 18 21

Solving Simple Inequalities 1-5 Solving Simple Inequalities Pre-Algebra Try This: Examples 2C and 2D Solve and graph each inequality. C. z – 6 < 15 + 6 + 6 Add 6 to both sides. z < 21 –21 –14 –7 0 7 14 21 D. 2 ≥ b 9 2 ≥ b 9 9 • 9 • Multiply both sides by 9. 18 ≥ b 0 3 6 9 12 15 18

Solving Simple Inequalities 1-5 Solving Simple Inequalities Pre-Algebra 1-5 Solving Simple Inequalities Pre-Algebra Try This: Example 3 Mr. Minturn will provide 130 cookies for the 7th grade. He has to buy the cookies in packages of 20. What is the least number of packages Mr. Minturn must buy to be sure to have enough cookies?

Solving Simple Inequalities 1-5 Solving Simple Inequalities Pre-Algebra Try This: Example 3 Understand the Problem The answer will be the number of packages of cookies a customer needs to purchase. List the important information: Cookies are sold in packages of 20 cookies. A customer needs to purchase 130 cookies. Show the relationship of the information: the number of packages of cookies to be purchased the number of cookies in one package 130 cookies • ≥

Solving Simple Inequalities 1-5 Solving Simple Inequalities Pre-Algebra Try This: Example 3 Continued 2 Make a Plan Use the relationship to write an inequality. Let x represent the number of packages of cookies. x • 20 cookies ≥ 130 cookies

Solving Simple Inequalities 1-5 Solving Simple Inequalities Pre-Algebra Try This: Example 3 Continued Solve 3 20x ≥ 130 20x ≥ 130 Divide both sides by 20. 20 20 x ≥ 6.5 At least 6.5 packages of cookies need to be purchased.

Solving Simple Inequalities 1-5 Solving Simple Inequalities Pre-Algebra Try This: Example 3 Continued 4 Look Back Because whole packages of cookies must be purchased, at least 7 packages of cookies must be purchased for the party.