6.1: Solve Linear Inequalities Do NOW Plug this into your graphing calculator and determine the equation. Then, identify whether type correlation it is. Years of Education Income 19 125,000 20 100,000 16 40,000 35,000 18 41,000 12 29,000 14 24,000 50,000 17 60,000 11/20/2018 8:03 AM 6.1: Solve Linear Inequalities
6.1: Solve Linear Inequalities Worksheet Key 11/20/2018 8:03 AM 6.1: Solve Linear Inequalities
6.1: Solve Linear Inequalities Worksheet Key 11/20/2018 8:03 AM 6.1: Solve Linear Inequalities
6.1: Solve Linear Inequalities Worksheet Key 11/20/2018 8:03 AM 6.1: Solve Linear Inequalities
6.1: Solve Linear Inequalities 11/20/2018 8:03 AM 6.1: Solve Linear Inequalities
SOLVE LINEAR INEQUALITIES Section 6.1 6 11/20/2018 8:03 AM
What do these signs mean? > Greater than ≥ Greater than OR equal to < Less than Less than OR equal to ≤ 11/20/2018 8:03 AM 6.1: Solve Linear Inequalities
6.1: Solve Linear Inequalities Key Words Greater Than, ‘ > ’ sign Greater Than Bigger Than Less Than, ‘ < ’ sign Less Than Smaller Than Greater Than or Equal to, ‘ > ’ sign Greater Than or Equal to Minimum of At least No less than Less Than or Equal to, ‘ < ’ sign Less Than or Equal to Maximum of Up to No More Than At Most 11/20/2018 8:03 AM 6.1: Solve Linear Inequalities
6.1: Solve Linear Inequalities Example 1 Your sister gave you her credit card and said that you could go shopping for a birthday present for your significant other. She said that you could spend no more than $125. Write the expression. What are some amounts that you could spend? 11/20/2018 8:03 AM 6.1: Solve Linear Inequalities
6.1: Solve Linear Inequalities Your Turn Your sister gave you her credit card and said that you could go shopping for a birthday present for your significant other. She said that you could spend at least $125. Write the expression. What are some amounts that you could spend? 11/20/2018 8:03 AM 6.1: Solve Linear Inequalities
6.1: Solve Linear Inequalities Example 2 Is (2, 4) a solution to the inequality y < 2x + 1? 11/20/2018 8:03 AM 6.1: Solve Linear Inequalities
6.1: Solve Linear Inequalities Example 3 Is (2, –4) a solution to the inequality y > 2x + 1? 11/20/2018 8:03 AM 6.1: Solve Linear Inequalities
6.1: Solve Linear Inequalities Example 4 Is (2, 5) a solution to the inequality y < 2x + 1? 11/20/2018 8:03 AM 6.1: Solve Linear Inequalities
6.1: Solve Linear Inequalities Your Turn Is (–3, –4) a solution to the inequality 2y > 3x + 1? 11/20/2018 8:03 AM 6.1: Solve Linear Inequalities
6.1: 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 8:03 AM 6.1: Solve Linear Inequalities
6.1: 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 8:03 AM 6.1: Solve Linear Inequalities
6.1: 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 8:03 AM 6.1: Solve Linear Inequalities
6.1: 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 11/20/2018 8:03 AM 6.1: Solve Linear Inequalities
6.1: Solve Linear Inequalities Example 5 Solve x < 6, graph and label as an inequality and internal notation. Make sure to shade the triangle for infinity | | 6 11/20/2018 8:03 AM 6.1: Solve Linear Inequalities
6.1: Solve Linear Inequalities Example 6 Solve 2x – 8 > 6, graph and label as an inequality and internal notation. | | 7 11/20/2018 8:03 AM 6.1: Solve Linear Inequalities
6.1: Solve Linear Inequalities Example 7 Solve , graph and label as an inequality and internal notation. | –4 1/4 | 11/20/2018 8:03 AM 6.1: Solve Linear Inequalities
6.1: Solve Linear Inequalities Your Turn Solve x + 4 > –5, graph and label as an inequality and internal notation. | –9 | 11/20/2018 8:03 AM 6.1: Solve Linear Inequalities
6.1: Solve Linear Inequalities Example 8 Solve –1 > x – 1/2, graph and label as an inequality and internal notation. | –1/2 | 11/20/2018 8:03 AM 6.1: Solve Linear Inequalities
6.1: Solve Linear Inequalities Example 9 Solve 5x + 3 > 4x + 5 , graph and label as an inequality. | | 2 11/20/2018 8:03 AM 6.1: Solve Linear Inequalities
6.1: Solve Linear Inequalities Your Turn Solve 5x – 6 < 4x – 4 , graph and label as an inequality. | | 2 11/20/2018 8:03 AM 6.1: Solve Linear Inequalities
6.1: Solve Linear Inequalities Rule REMEMBER: When we NEGATIVE DIVIDE, we FLIP THE SIGN 11/20/2018 8:03 AM 6.1: Solve Linear Inequalities
Example 10 Solve –3x > 24, graph and label as an inequality and internal notation. When we negative divide, we flip the sign | –8 | 11/20/2018 8:03 AM 6.1: Solve Linear Inequalities
Example 11 Solve –3/4x > 18, graph and label as an inequality and internal notation. When we negative divide, we flip the sign | –24 | 11/20/2018 8:03 AM 6.1: Solve Linear Inequalities
6.1: Solve Linear Inequalities Example 12 Solve x + 8 > 4x + 17, graph and label as an inequality | –3 | 11/20/2018 8:03 AM 6.1: Solve Linear Inequalities
6.1: Solve Linear Inequalities Your Turn Solve , write the answer as an inequality, and graph on a number line | –36 | 11/20/2018 8:03 AM 6.1: Solve Linear Inequalities
6.1: Solve Linear Inequalities Do NOW Tell whether the order pair is a solution to the inequality. Show all work: Solve the inequalities, graph, and write the answer in Inequality and Interval Notation form 11/20/2018 8:03 AM 6.1: Solve Linear Inequalities
6.1: Solve Linear Inequalities Worksheet Key 11/20/2018 8:03 AM 6.1: Solve Linear Inequalities
6.1: Solve Linear Inequalities Worksheet Key 11/20/2018 8:03 AM 6.1: Solve Linear Inequalities
6.1: Solve Linear Inequalities Quiz 11/20/2018 8:03 AM 6.1: Solve Linear Inequalities
Graphing Inequalities Draw the graph either applying slope–intercept or quick graph form When using “cover–up,” if there is a negative coefficient in the y, flip the direction of the graph Determine what the sign is and graph the line Dotted Line: Greater, Less, or not–equal to Solid Line: Greater then OR equal to, Less than OR equal to, Equal to Shade above or below the line by looking at inequality 11/20/2018 8:03 AM 6.1: Solve Linear Inequalities
Graphing Inequalities > > Greater than Greater than OR equal to < < Less than Less than OR equal to Dotted Line Solid Line
6.1: Solve Linear Inequalities Example 13 Graph x < 4 11/20/2018 8:03 AM 6.1: Solve Linear Inequalities
6.1: Solve Linear Inequalities Example 14 Graph x > 1 11/20/2018 8:03 AM 6.1: Solve Linear Inequalities
6.1: Solve Linear Inequalities Your Turn Graph x < 0 11/20/2018 8:03 AM 6.1: Solve Linear Inequalities
Steps in Graphing shade Greater Than u > >
Steps in Graphing shade own < < Less Than
6.1: Solve Linear Inequalities Example 15 Graph y < –2 11/20/2018 8:03 AM 6.1: Solve Linear Inequalities
6.1: Solve Linear Inequalities Example 16 Graph y < x + 1 11/20/2018 8:03 AM 6.1: Solve Linear Inequalities
Example 16 Calculator Check Graph y < x + 1 11/20/2018 8:03 AM 6.1: Solve Linear Inequalities
6.1: Solve Linear Inequalities Example 17 Graph 2x + 2y < –2 11/20/2018 8:03 AM 6.1: Solve Linear Inequalities
6.1: Solve Linear Inequalities Your Turn Graph 3x + y > –2 11/20/2018 8:03 AM 6.1: Solve Linear Inequalities
6.1: Solve Linear Inequalities Example 18 Graph 2x – y < 2 11/20/2018 8:03 AM 6.1: Solve Linear Inequalities
6.1: Solve Linear Inequalities Example 19 Graph 2x – 4y < 8 11/20/2018 8:03 AM 6.1: Solve Linear Inequalities
6.1: Solve Linear Inequalities Your Turn Graph 3x – 2y < 8 11/20/2018 8:03 AM 6.1: Solve Linear Inequalities
6.1: Solve Linear Inequalities Assignment Worksheet 11/20/2018 8:03 AM 6.1: Solve Linear Inequalities