write out the compound inequalities. 1.x is at most -2 or at least 0 2.y is less than 9 and greater...
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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