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.

3. -22 < -6x – 4 < 2

4. -4x – 6 > 10 or 6x + 4 > -2

Warm Up6.3

x < -2 or x > 0

1 < x < 9

-1 < x < 3

x < -4 or x > -1

Objectives:1. Solve absolute value equations2. Solve absolute value inequalities Vocabulary: absolute value

Solving Absolute Value Equations and Inequalities6.4

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 x > c

“or”

<, <: less thAND

>, >: greatORThe 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 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 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 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 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 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 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|> 4Solving 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 > 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 x > c “or”

-5 < x < 27/5

Exit Slippg. 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, 55-57 (graph 55-57)

Algebra 1