Algebra I Chapter 6: Solving and Graphing Linear Inequalities
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1 Algebra I Chapter 6: Solving and Graphing Linear Inequalities Jun 10 9:21 AM Chapter 6 Lesson 1 Solve Inequalities Using Addition and Subtraction Vocabulary Words to Review: Inequality Solution of an Inequality Jun 13 1:21 PM 1
2 Example 1: Write and Graph an Inequality Graphing Inequalities Hints: 1. Always make sure the variable is on the left. (If you can say it, you can graph it. x>3 means x is greater than 3.) 2. Put at least 5 numbers on your line. The number of importance and two on each side of it. 3. Use open circles for > and <. Used closed circles for > and <. 4. Make your directional arrows dark! :) Jun 10 9:24 AM Example 2: Write Inequalities from Graphs Graphing Inequalities Hints: 1. Always make sure the variable is on the left. (If you can say it, you can graph it. x>3 means x is greater than 3.) 2. Put at least 5 numbers on your line. The number of importance and two on each side of it. 3. Use open circles for > and <. Used closed circles for > and <. 4. Make your directional arrows dark! :) Aug 28 1:44 PM 2
3 Example 3: Solve an Inequality Using Addition Hint: The sign of the inequality will not change if you use the addition or subtraction properties. Aug 28 1:47 PM Example 4: Solve an Inequality Using Subtraction Hint: The sign of the inequality will not change if you use the addition or subtraction properties. Sep 9 10:53 AM 3
4 Example 5: Solve a Real World Problem Sep 20 1:09 PM Chapter 6 Lesson 2 Solve Inequalities Using Multiplication and Division Vocabulary Words to Review: Inequality Equivalent Inequalities Aug 28 2:08 PM 4
5 Example 1: Solve an Inequality Using Multiplication Graphing Inequalities Hints: 1. Always make sure the variable is on the left. (If you can say it, you can graph it. x>3 means x is greater than 3.) 2. Put at least 5 numbers on your line. The number of importance and two on each side of it. 3. Use open circles for > and <. Used closed circles for > and <. 4. Make your directional arrows dark! :) Aug 29 8:29 AM Example 2: Solve an Inequality Using Multiplication Graphing Inequalities Hints: 1. Always make sure the variable is on the left. (If you can say it, you can graph it. x>3 means x is greater than 3.) 2. Put at least 5 numbers on your line. The number of importance and two on each side of it. 3. Use open circles for > and <. Used closed circles for > and <. 4. Make your directional arrows dark! :) Hint: If you divide or multiply by a negative number, the inequality symbol will flip! Aug 29 8:29 AM 5
6 Example 3: Solve an Inequality Using Division Graphing Inequalities Hints: 1. Always make sure the variable is on the left. (If you can say it, you can graph it. x>3 means x is greater than 3.) 2. Put at least 5 numbers on your line. The number of importance and two on each side of it. 3. Use open circles for > and <. Used closed circles for > and <. 4. Make your directional arrows dark! :) Hint: If you divide or multiply by a negative number, the inequality symbol will flip! Aug 29 8:29 AM Example 4: Standardized Test Practice Sep 20 1:11 PM 6
7 Example 5: Solve a Real World Problem Sep 20 1:11 PM Chapter 6 Lesson 3 Solve Multi Step Inequalities Vocabulary Words to Review: Inequality Aug 30 12:52 PM 7
8 Example 1: Solve a Two Step Inequality Graphing Inequalities Hints: 1. Always make sure the variable is on the left. (If you can say it, you can graph it. x>3 means x is greater than 3.) 2. Put at least 5 numbers on your line. The number of importance and two on each side of it. 3. Use open circles for > and <. Used closed circles for > and <. 4. Make your directional arrows dark! :) Hint: If you divide or multiply by a negative number, the inequality symbol will flip! Aug 30 1:08 PM Example 2: Solve a Multi Step Inequality Graphing Inequalities Hints: 1. Always make sure the variable is on the left. (If you can say it, you can graph it. x>3 means x is greater than 3.) 2. Put at least 5 numbers on your line. The number of importance and two on each side of it. 3. Use open circles for > and <. Used closed circles for > and <. 4. Make your directional arrows dark! :) Hint: If you divide or multiply by a negative number, the inequality symbol will flip! Aug 30 1:08 PM 8
9 Example 3: Solve a Multi Step Inequality Graphing Inequalities Hints: 1. Always make sure the variable is on the left. (If you can say it, you can graph it. x>3 means x is greater than 3.) 2. Put at least 5 numbers on your line. The number of importance and two on each side of it. 3. Use open circles for > and <. Used closed circles for > and <. 4. Make your directional arrows dark! :) Hint: If you divide or multiply by a negative number, the inequality symbol will flip! Aug 30 1:08 PM Example 4: Identify the Number of Solutions of an Inequality What to do when the variable "drops out"? If the resulting inequality is TRUE, then the answer is ALL REAL NUMBERS. (There is an infinite number of possible values for the variable that will be true.) If the resulting inequality is NOT TRUE, then the answer is NO SOLUTION. (There are no numbers that could make the inequality true.) Aug 30 1:08 PM 9
10 Example 5: Solve a Multi Step Problem Sep 24 12:46 PM Chapter 6 Lesson 4 Solve Compound Inequalities Vocabulary AND Notice the smaller number is always on the left! OR x<3 or x>7 Aug 30 12:52 PM 10
11 Example 1: Write and Graph Compound Inequalities Hint: and inequalities look similar to this: 3 < x < 2 and inequality graphs look similar to this: or inequalities look similar to this: x < 3 or x > 2 or inequality graphs look similar to this: Aug 30 1:55 PM Example 2: Write and Graph a Real World Compound Inequality Aug 30 1:56 PM 11
12 Example 3: Solve a Compound Inequality with and When Solving Compound Inequalities with and 1. Separate the statement into the two different inequalities. 2. Solve each inequality. (Reminder: IF you multiply or divide by a negative number, the inequality symbol MUST flip!) 3. Remember that the graph should be everything between two numbers. Aug 30 1:56 PM Example 4: Solve a Compound Inequality with and When Solving Compound Inequalities with and 1. Separate the statement into the two different inequalities. 2. Solve each inequality. (Reminder: IF you multiply or divide by a negative number, the inequality symbol MUST flip!) 3. Remember that the graph should be everything between two numbers. Sep 20 1:24 PM 12
13 Example 5: Solve a Compound Inequality with or When Solving Compound Inequalities with or 1. Solve each inequality. (Reminder: IF you multiply or divide by a negative number, the inequality symbol MUST flip!) 2. Remember that the graph should go in opposite directions. Sep 20 1:25 PM Example 6: Solve a Multi Step Problem Oct 30 2:10 PM 13
14 Chapter 6 Lesson 5 Solve Absolute Value Equations Vocabulary Words to Review: Absolute Value Aug 30 12:52 PM Example 1: Solve an Absolute Value Equation Reminder: absolute value refers to the distance between a number and 0. Sep 25 7:22 AM 14
15 Example 2: Solve an Absolute Value Equation When Solving an Absolute Value Equation: 1. Rewrite the absolute value equation as two equations. *For the first equation: Drop the bars. Make the answer part positive. *For the second equation: Drop the bars. Make the answer part negative. 2. Solve each equation. 3. Check your answers. Sep 20 12:44 PM Example 3: Rewrite an Absolute Value Equation When Solving an Absolute Value Equation: 1. Add, subtract, multiply, or divide until only the absolute value part of the equation remains on one side or the equation. 2. Rewrite the absolute value equation as two equations. *For the first equation: Drop the bars. Make the answer part positive. *For the second equation: Drop the bars. Make the answer part negative. 3. Solve each equation. 4. Check your answers. Sep 20 1:32 PM 15
16 Example 4: Decide if an Equation has No Soltuion When Solving an Absolute Value Equation: 1. Add, subtract, multiply, or divide until only the absolute value part of the equation remains on one side or the equation. 2. Rewrite the absolute value equation as two equations. *For the first equation: Drop the bars. Make the answer part positive. *For the second equation: Drop the bars. Make the answer part negative. 3. Solve each equation. 4. Check your answers. Sep 20 1:32 PM Example 5: Use Absolute Deviation Sep 20 1:33 PM 16
17 Chapter 6 Lesson 6 Solve Absolute Value Inequalities Vocabulary Words to Review: Absolute Value Equivalent Inequalities Compound Inequalities Absolute Deviation Mean Aug 30 12:52 PM Example 1: Solve Absolute Value Inequalities When Graphing Absolute Value Equations: 1. Add, subtract, multiply, or divide until only the absolute value part of the equation remains on one side or the equation. 2. Rewrite the absolute value equation as two equations. *For the first equation: Drop the bars. Make the answer part positive. *For the second equation: Drop the bars. FLIP THE INEQUALITY SYMBOL! Make the answer part negative. 3. Solve each equation. Check your answers. 4. The result will be an and or or situation. Graph the result. Sep 20 12:45 PM 17
18 Example 2: Solve an Absolute Value Inequality When Graphing Absolute Value Equations: 1. Add, subtract, multiply, or divide until only the absolute value part of the equation remains on one side or the equation. 2. Rewrite the absolute value equation as two equations. *For the first equation: Drop the bars. Make the answer part positive. *For the second equation: Drop the bars. FLIP THE INEQUALITY SYMBOL! Make the answer part negative. 3. Solve each equation. Check your answers. 4. The result will be an and or or situation. Graph the result. Sep 20 1:34 PM Example 3: Solve an Absolute Value Inequality When Graphing Absolute Value Equations: 1. Add, subtract, multiply, or divide until only the absolute value part of the equation remains on one side or the equation. 2. Rewrite the absolute value equation as two equations. *For the first equation: Drop the bars. Make the answer part positive. *For the second equation: Drop the bars. FLIP THE INEQUALITY SYMBOL! Make the answer part negative. 3. Solve each equation. Check your answers. 4. The result will be an and or or situation. Graph the result. Sep 20 1:35 PM 18
19 Example 4: Solve a Multi Step Problem Sep 20 1:35 PM Chapter 6 Lesson 7 Graph Linear Inequalities in Two Variables Vocabulary Aug 30 12:52 PM 19
20 Example 1: Standardized Test Practice Sep 20 12:49 PM Example 2: Graph a Linear Inequality in Two Variables Most people like to do this by solving for y. You could also use intercepts or a table. Most people use (0,0) because it is easy to work with! Remind me to share a shortcut with you! Sep 20 1:37 PM 20
21 Example 3: Graph a Linear Inequality in Two Variables Most people like to do this by solving for y. You could also use intercepts or a table. Most people use (0,0) because it is easy to work with! Remind me to share a shortcut with you! Sep 20 1:37 PM Example 4: Graph a Linear Inequality in One Variable Most people like to do this by solving for y. You could also use intercepts or a table. Most people use (0,0) because it is easy to work with! Remind me to share a shortcut with you! Sep 20 1:37 PM 21
22 Example 5: Graph a Linear Inequality in One Variable Most people like to do this by solving for y. You could also use intercepts or a table. Most people use (0,0) because it is easy to work with! Remind me to share a shortcut with you! Sep 20 1:38 PM Example 6: Solve a Multi Step Problem Dec 11 9:18 AM 22
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