Write out the compound inequalities. 1.x is at most -2 or at least 0 2.y is less than 9 and greater than or equal to 1 Solve the inequalities < -6x – 4 < x – 6 > 10 or 6x + 4 > -2 Warm Up 6.3 x 0 1 < x < 9 -1 < x < 3 x -1

Objectives: 1.Solve absolute value equations 2.Solve absolute value inequalities Vocabulary: absolute value Solving Absolute Value Equations and Inequalities 6.4

Solve and graph these inequalities: Example 2 Solving an Absolute Value Inequality Solving Absolute Inequalities: 1.Isolate the absolute value. 2.Set up the problem appropriately: “and” or “or.” 3.Solve the inequalities. 4.Check both answers. Absolute inequality rules: |x|< c, then –c < x < c “and” |x|> c, then x c “or” <, <: less thAND >, >: greatOR The setup does not need absolute value symbols!

Solve and graph the inequality: Example 2 Solving an Absolute Value Inequality |x|< 5 Absolute inequality rules: |x|< c, then –c < x < c “and” |x|> c, then x c “or” Solving Absolute Inequalities: 1.Isolate the absolute value. 2.Set up the problem appropriately: “and” or “or.” 3.Solve the inequalities. 4.Check both answers. <, <: Less thAND >, >: GreatOR -5 < x < 5

Solve and graph the inequalities: Example 2 Solving an Absolute Value Inequality |4x – 9| < 21 |3x – 2| > 18 Absolute inequality rules: |x|< c, then –c < x < c “and” |x|> c, then x c “or” Solving Absolute Inequalities: 1.Isolate the absolute value. 2.Set up the problem appropriately: “and” or “or.” 3.Solve the inequalities. 4.Check both answers. <, <: Less thAND >, >: GreatOR -3 < x < 15/2 x > 20/3 or x < -16/3

Solve and graph the inequality: Example 2 Solving an Absolute Value Inequality |10 – 4x|≤ 2 Absolute inequality rules: |x|< c, then –c < x < c “and” |x|> c, then x c “or” Solving Absolute Inequalities: 1.Isolate the absolute value. 2.Set up the problem appropriately: “and” or “or.” 3.Solve the inequalities. 4.Check both answers. <, <: Less thAND >, >: GreatOR 3 > x > 2 2 < x < 3

Solve and graph the inequality: Example 2 Solving an Absolute Value Inequality |x + 2| – 5 ≥ 8 Absolute inequality rules: |x|< c, then –c < x < c “and” |x|> c, then x c “or” Solving Absolute Inequalities: 1.Isolate the absolute value. 2.Set up the problem appropriately: “and” or “or.” 3.Solve the inequalities. 4.Check both answers. <, <: Less thAND >, >: GreatOR x > 11 or x < -15

Solve and graph the inequality: Example 2 Solving an Absolute Value Inequality |3x + 2| – 1 ≥ 10 Absolute inequality rules: |x|< c, then –c < x < c “and” |x|> c, then x c “or” Solving Absolute Inequalities: 1.Isolate the absolute value. 2.Set up the problem appropriately: “and” or “or.” 3.Solve the inequalities. 4.Check both answers. <, <: Less thAND >, >: GreatOR x > 3 or x < -13/3

Solve and graph the inequality: Example 2 Solving an Absolute Value Inequality |2x + 5| – 1 < 6 Absolute inequality rules: |x|< c, then –c < x < c “and” |x|> c, then x c “or” Solving Absolute Inequalities: 1.Isolate the absolute value. 2.Set up the problem appropriately: “and” or “or.” 3.Solve the inequalities. 4.Check both answers. <, <: Less thAND >, >: GreatOR -6 < x < 1

Solve and graph the inequality: Example 2 Solving an Absolute Value Inequality |2x + 3|> 4 Solving Absolute Inequalities: 1.Isolate the absolute value. 2.Set up the problem appropriately: “and” or “or.” 3.Solve the inequalities. 4.Check both answers. <, <: Less thAND >, >: GreatOR Absolute inequality rules: |x|< c, then –c < x < c “and” |x|> c, then x c “or” x > 1/2 or x < -7/2

Solve and graph the inequality: Example 2 Solving an Absolute Value Inequality |5x – 1| – 10 < 16 Solving Absolute Inequalities: 1.Isolate the absolute value. 2.Set up the problem appropriately: “and” or “or.” 3.Solve the inequalities. 4.Check both answers. <, <: Less thAND >, >: GreatOR Absolute inequality rules: |x|< c, then –c < x < c “and” |x|> c, then x c “or” -5 < x < 27/5

Exit Slip pg. 356 #15-17 in textbook Show work Solve and graph Algebra 1 Raise your hand when you are done to receive credit and get the assignment!

Algebra 1 Assignment due tomorrow: pg. 357 #40-42, (graph 55-57) Algebra 1