1.6: Solve Linear Inequalities Page 30 3) 5) 7) y = –3x + 26; y = 5 9) y = –6/5x + 31/5; y = 11 11) y = 3/2x – 21/2; y = –3 13) y = 7/4x – 11/4; y = 6 15) C 17) There are two y’s on both sides 19) 21) 23) 25) 29) Omit 31) omit 11/20/2018 8:04 AM 1.6: Solve Linear Inequalities

1.6: Solve Linear Inequalities 11/20/2018 8:04 AM 1.6: Solve Linear Inequalities

1.6: Solve Linear Inequalities Page 37 3) t = 0.5h 5) d = 90 miles 7) P = 54 feet 9) w = 20 meters 11) y = 4x + 11 13) y = –10x + 46 15) D 21) B 24) 156.25 mi/hr 11/20/2018 8:04 AM 1.6: Solve Linear Inequalities

SOLVE LINEAR INEQUALITIES Section 1.6 4 11/20/2018 8:04 AM

What do these signs mean? > Greater than ≥ Greater than OR equal to < Less than Less than OR equal to ≤ 11/20/2018 8:04 AM 1.6: Solve Linear Inequalities

1.6: Solve Linear Inequalities Definitions Inequality is an equation where the variable does not equal to each other >, <, or ≠ requires the dot being OPEN >, <, or = required the dot being CLOSED hole 11/20/2018 8:04 AM 1.6: Solve Linear Inequalities

1.6: Solve Linear Inequalities X typically comes first or is in the middle of the compound > represents greater than < represents less than <, > represents greater than or equal to, less than or equal to 11/20/2018 8:04 AM 1.6: Solve Linear Inequalities

1.6: Solve Linear Inequalities Interval Notation Smallest number, bigger number Brackets [ , ] represents greater than or equal to, less than or equal to Parenthesis ( , ) represents greater than or less than On the ends, extremes use infinity: ∞; always deals with parenthesis 11/20/2018 8:04 AM 1.6: Solve Linear Inequalities

1.6: Solve Linear Inequalities Set-Builder Notation A representative set is a collection of items { x | x > 0 } reads “the set of all x such that x is greater than zero” Applies to inequalities 11/20/2018 8:04 AM 1.6: Solve Linear Inequalities

1.6: Solve Linear Inequalities Steps Put the variables onto one side Divide the number(s) in front of the variable Graph on a number line based on the inequality given Follow the arrow of the expression IF the variable comes first Less thAND: Shade towards or INSIDE GreatOR: Shade away or OUTSIDE REMEMBER: When we NEGATIVE DIVIDE, we FLIP THE SIGN 11/20/2018 8:04 AM 1.6: Solve Linear Inequalities

1.6: Solve Linear Inequalities Example 1 Solve 2x < 12, graph and label as an inequality, set-builder notation, and internal notation. Make sure to shade the triangle for infinity | | 6 11/20/2018 8:04 AM 1.6: Solve Linear Inequalities

1.6: Solve Linear Inequalities Example 2 Solve x + 8 > 4x + 17, graph and label as an inequality, set-builder notation, and internal notation. | –3 | 11/20/2018 8:04 AM 1.6: Solve Linear Inequalities

1.6: Solve Linear Inequalities Your Turn Solve –2 > –12x + 8, graph and label as an inequality, set-builder notation, and internal notation. | 5/6 11/20/2018 8:04 AM 1.6: Solve Linear Inequalities

1.6: Solve Linear Inequalities Example 3 Solve –4 < 6x – 10 < 14, graph and label as an inequality, set-builder notation, and internal notation. | | 1 | 4 11/20/2018 8:04 AM 1.6: Solve Linear Inequalities

1.6: Solve Linear Inequalities Your Turn Solve 0 < 3/4x + 3 < 4, graph and label as an inequality, set-builder notation, and internal notation. | –4 | | 4/3 11/20/2018 8:04 AM 1.6: Solve Linear Inequalities

1.6: Solve Linear Inequalities Example 4 Solve 2x – 1 < –7 or 4x + 3 > 7, graph and label as an inequality, set-builder notation, and internal notation. | –3 | | 1 11/20/2018 8:04 AM 1.6: Solve Linear Inequalities

1.6: Solve Linear Inequalities Example 5 Solve x + 5 < 10 OR x – 2 > 1, graph and label as an inequality, set-builder notation, and internal notation. | | 3 | 5 11/20/2018 8:04 AM 1.6: Solve Linear Inequalities

1.6: Solve Linear Inequalities Example 6 Solve 5x – 10 < 5(x + 2) 11/20/2018 8:04 AM 1.6: Solve Linear Inequalities

1.6: Solve Linear Inequalities Your Turn Solve 6(x – 2) > 3(2x – 1) 11/20/2018 8:04 AM 1.6: Solve Linear Inequalities

1.6: Solve Linear Inequalities Example 7 A lizard has a temperature that ranges from 18°C to 34°C. Write the range of temperatures as a compound inequality. Then write an inequality giving the temperature range in degrees in Fahrenheit. The conversion of Celsius to Fahrenheit is 5/9(F – 32). 11/20/2018 8:04 AM 1.6: Solve Linear Inequalities

1.6: Solve Linear Inequalities Your Turn In Illinois, the lowest temperature on record is –36°F in January 1999. The highest temperature was recorded in East St. Louis at 117°F. Determine the range of temperatures in Celsius. The conversion of Celsius is 9/5C + 32. 11/20/2018 8:04 AM 1.6: Solve Linear Inequalities

1.6: Solve Linear Inequalities Assignment Pg 44: 3-15 odd, 23-45 odd, 49-51 all, 53, 56 29-45: With the inequality, write out in set-builder notation and interval notation 11/20/2018 8:04 AM 1.6: Solve Linear Inequalities