DO NOW Plug this into your graphing calculator

WORKSHEET KEY 12/16/2021 11: 37 PM 6. 1: Solve Linear Inequalities

12/16/2021 11: 37 PM 6. 1: Solve Linear Inequalities

SOLVE LINEAR INEQUALITIES Section 6. 1 12/16/2021 11: 37 PM 6. 1: Solve Linear

WHAT DO THESE SIGNS MEAN? Greater than OR equal to Less than OR equal

KEY WORDS A. Greater Than, ‘ > ’ sign 1. Greater Than 2. Bigger

EXAMPLE 1 Your sister gave you her credit card and said that you could

YOUR TURN Your sister gave you her credit card and said that you could

EXAMPLE 2 Is (2, 4) a solution to the inequality y < 2 x

EXAMPLE 3 Is (2, – 4) a solution to the inequality y > 2

EXAMPLE 4 Is (2, 5) a solution to the inequality y < 2 x

YOUR TURN Is (– 3, – 4) a solution to the inequality 2 y

DEFINITIONS A. Inequality is an equation where the variable does not equal to each

INEQUALITIES A. X typically comes first or is in the middle of the compound

INTERVAL NOTATION A. Smallest number, bigger number B. Brackets [ , ] represents greater

STEPS A. Put the variables onto one side B. Divide the number(s) in front

EXAMPLE 5 Solve x < 6, graph and label as an inequality and internal

EXAMPLE 6 Solve 2 x – 8 > 6, graph and label as an

EXAMPLE 7 Solve , graph and label as an inequality and internal notation. |

YOUR TURN Solve x + 4 > – 5, graph and label as an

EXAMPLE 8 Solve – 1 > x – 1/2, graph and label as an

EXAMPLE 9 Solve 5 x + 3 > 4 x + 5 , graph

YOUR TURN Solve 5 x – 6 < 4 x – 4 , graph

RULE A. REMEMBER: When we NEGATIVE DIVIDE, we FLIP THE SIGN 12/16/2021 11: 38

EXAMPLE 10 Solve – 3 x > 24, graph and label as an inequality

EXAMPLE 11 Solve – 3/4 x > 18, graph and label as an inequality

EXAMPLE 12 Solve x + 8 > 4 x + 17, graph and label

YOUR TURN Solve , write the answer as an inequality, and graph on a

DO NOW Tell whether the order pair is a solution to the inequality. Show

WORKSHEET KEY 12/16/2021 11: 38 PM 6. 1: Solve Linear Inequalities

QUIZ 12/16/2021 11: 38 PM 6. 1: Solve Linear Inequalities

GRAPHING INEQUALITIES A. Draw the graph either applying slope–intercept or quick graph form 1.

GRAPHING INEQUALITIES Greater than Less than Dotted Line Greater than OR equal to Less

EXAMPLE 13 Graph x < 4 12/16/2021 11: 38 PM 6. 1: Solve Linear

EXAMPLE 14 Graph x > 1 12/16/2021 11: 38 PM 6. 1: Solve Linear

YOUR TURN Graph x < 0 12/16/2021 11: 38 PM 6. 1: Solve Linear

STEPS IN GRAPHING shade u > Greater Than

EXAMPLE 15 Graph y < – 2 12/16/2021 11: 38 PM 6. 1: Solve

EXAMPLE 16 Graph y < x + 1 12/16/2021 11: 38 PM 6. 1:

EXAMPLE 16 CALCULATOR CHECK Graph y < x + 1 12/16/2021 11: 38 PM

EXAMPLE 17 Graph 2 x + 2 y < – 2 12/16/2021 11: 38

YOUR TURN Graph 3 x + y > – 2 12/16/2021 11: 39 PM

EXAMPLE 18 Graph 2 x – y < 2 12/16/2021 11: 39 PM 6.

EXAMPLE 19 Graph 2 x – 4 y < 8 12/16/2021 11: 39 PM

YOUR TURN Graph 3 x – 2 y < 8 12/16/2021 11: 39 PM

ASSIGNMENT Worksheet 12/16/2021 11: 39 PM 6. 1: Solve Linear Inequalities

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DO NOW Plug this into your graphing calculator and determine the equation. Then, identify whether type correlation it is. 12/16/2021 11: 37 PM Years of Education Income 19 20 16 16 18 12 14 12 16 17 125, 000 100, 000 40, 000 35, 000 41, 000 29, 000 35, 000 24, 000 50, 000 6. 1: Solve Linear Inequalities

WORKSHEET KEY 12/16/2021 11: 37 PM 6. 1: Solve Linear Inequalities

12/16/2021 11: 37 PM 6. 1: Solve Linear Inequalities

SOLVE LINEAR INEQUALITIES Section 6. 1 12/16/2021 11: 37 PM 6. 1: Solve Linear Inequalities 6

WHAT DO THESE SIGNS MEAN? Greater than OR equal to Less than OR equal to 12/16/2021 11: 37 PM 6. 1: Solve Linear Inequalities

KEY WORDS A. Greater Than, ‘ > ’ sign 1. Greater Than 2. Bigger Than B. Less Than, ‘ < ’ sign 1. Less Than 2. Smaller Than C. Greater Than or Equal to, ‘ > ’ sign 1. 2. 3. 4. Greater Than or Equal to Minimum of At least No less than D. Less Than or Equal to, ‘ < ’ sign 1. 2. 3. 4. 5. Less Than or Equal to Maximum of Up to No More Than At Most 12/16/2021 11: 37 PM 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? 12/16/2021 11: 37 PM 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? 12/16/2021 11: 37 PM 6. 1: Solve Linear Inequalities

EXAMPLE 2 Is (2, 4) a solution to the inequality y < 2 x + 1? 12/16/2021 11: 37 PM 6. 1: Solve Linear Inequalities

EXAMPLE 3 Is (2, – 4) a solution to the inequality y > 2 x + 1? 12/16/2021 11: 37 PM 6. 1: Solve Linear Inequalities

EXAMPLE 4 Is (2, 5) a solution to the inequality y < 2 x + 1? 12/16/2021 11: 37 PM 6. 1: Solve Linear Inequalities

YOUR TURN Is (– 3, – 4) a solution to the inequality 2 y > 3 x + 1? 12/16/2021 11: 37 PM 6. 1: Solve Linear Inequalities

DEFINITIONS A. Inequality is an equation where the variable does not equal to each other B. >, <, or ≠ requires the dot being OPEN C. >, <, or = required the dot being CLOSED hole 12/16/2021 11: 37 PM 6. 1: Solve Linear Inequalities

INEQUALITIES A. X typically comes first or is in the middle of the compound B. > represents greater than C. < represents less than D. <, > represents greater than or equal to, less than or equal to 12/16/2021 11: 37 PM 6. 1: Solve Linear Inequalities

INTERVAL NOTATION A. Smallest number, bigger number B. Brackets [ , ] represents greater than or equal to, less than or equal to C. Parenthesis ( , ) represents greater than or less than D. On the ends, extremes use infinity: ∞; always deals with parenthesis 12/16/2021 11: 38 PM 6. 1: Solve Linear Inequalities

STEPS A. Put the variables onto one side B. Divide the number(s) in front of the variable C. Graph on a number line based on the inequality given D. Follow the arrow of the expression IF the variable comes first 12/16/2021 11: 38 PM 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 | 0 12/16/2021 11: 38 PM 6. 1: Solve Linear Inequalities | 6

EXAMPLE 6 Solve 2 x – 8 > 6, graph and label as an inequality and internal notation. | 0 12/16/2021 11: 38 PM 6. 1: Solve Linear Inequalities | 7

EXAMPLE 7 Solve , graph and label as an inequality and internal notation. | – 4 1/4 12/16/2021 11: 38 PM | 0 6. 1: Solve Linear Inequalities

YOUR TURN Solve x + 4 > – 5, graph and label as an inequality and internal notation. | – 9 12/16/2021 11: 38 PM | 0 6. 1: Solve Linear Inequalities

EXAMPLE 8 Solve – 1 > x – 1/2, graph and label as an inequality and internal notation. | – 1/2 12/16/2021 11: 38 PM | 0 6. 1: Solve Linear Inequalities

EXAMPLE 9 Solve 5 x + 3 > 4 x + 5 , graph and label as an inequality. | 0 12/16/2021 11: 38 PM 6. 1: Solve Linear Inequalities | 2

YOUR TURN Solve 5 x – 6 < 4 x – 4 , graph and label as an inequality. | 0 12/16/2021 11: 38 PM 6. 1: Solve Linear Inequalities | 2

RULE A. REMEMBER: When we NEGATIVE DIVIDE, we FLIP THE SIGN 12/16/2021 11: 38 PM 6. 1: Solve Linear Inequalities

EXAMPLE 10 Solve – 3 x > 24, graph and label as an inequality and internal notation. When we negative divide, we flip the sign | – 8 12/16/2021 11: 38 PM | 0 6. 1: Solve Linear Inequalities

EXAMPLE 11 Solve – 3/4 x > 18, graph and label as an inequality and internal notation. When we negative divide, we flip the sign | – 24 12/16/2021 11: 38 PM | 0 6. 1: Solve Linear Inequalities

EXAMPLE 12 Solve x + 8 > 4 x + 17, graph and label as an inequality | – 3 12/16/2021 11: 38 PM | 0 6. 1: Solve Linear Inequalities

YOUR TURN Solve , write the answer as an inequality, and graph on a number line | – 36 12/16/2021 11: 38 PM | 0 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 12/16/2021 11: 38 PM 6. 1: Solve Linear Inequalities

WORKSHEET KEY 12/16/2021 11: 38 PM 6. 1: Solve Linear Inequalities

QUIZ 12/16/2021 11: 38 PM 6. 1: Solve Linear Inequalities

GRAPHING INEQUALITIES A. Draw the graph either applying slope–intercept or quick graph form 1. When using “cover–up, ” if there is a negative coefficient in the y, flip the direction of the graph B. Determine what the sign is and graph the line 1. Dotted Line: Greater, Less, or not–equal to 2. Solid Line: Greater then OR equal to, Less than OR equal to, Equal to C. Shade above or below the line by looking at inequality 12/16/2021 11: 38 PM 6. 1: Solve Linear Inequalities

GRAPHING INEQUALITIES Greater than Less than Dotted Line Greater than OR equal to Less than OR equal to Solid Line

EXAMPLE 13 Graph x < 4 12/16/2021 11: 38 PM 6. 1: Solve Linear Inequalities

EXAMPLE 14 Graph x > 1 12/16/2021 11: 38 PM 6. 1: Solve Linear Inequalities

YOUR TURN Graph x < 0 12/16/2021 11: 38 PM 6. 1: Solve Linear Inequalities

STEPS IN GRAPHING shade u > Greater Than

STEPS IN GRAPHING < shade own Less Than

EXAMPLE 15 Graph y < – 2 12/16/2021 11: 38 PM 6. 1: Solve Linear Inequalities

EXAMPLE 16 Graph y < x + 1 12/16/2021 11: 38 PM 6. 1: Solve Linear Inequalities

EXAMPLE 16 CALCULATOR CHECK Graph y < x + 1 12/16/2021 11: 38 PM 6. 1: Solve Linear Inequalities

EXAMPLE 17 Graph 2 x + 2 y < – 2 12/16/2021 11: 38 PM 6. 1: Solve Linear Inequalities

YOUR TURN Graph 3 x + y > – 2 12/16/2021 11: 39 PM 6. 1: Solve Linear Inequalities

EXAMPLE 18 Graph 2 x – y < 2 12/16/2021 11: 39 PM 6. 1: Solve Linear Inequalities

EXAMPLE 19 Graph 2 x – 4 y < 8 12/16/2021 11: 39 PM 6. 1: Solve Linear Inequalities

YOUR TURN Graph 3 x – 2 y < 8 12/16/2021 11: 39 PM 6. 1: Solve Linear Inequalities

ASSIGNMENT Worksheet 12/16/2021 11: 39 PM 6. 1: Solve Linear Inequalities