Absolute Value Inequalities

An absolute value inequality is

• an inequality that contains an absolute value expression
• impossible to solve
• an equation that contains an absolute value expression
• always going to have two solutions

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.3

Which compound inequality represents the graph?

• m < -1 OR m > 2
• -1 < m < 2
• m > -1 OR m < 2

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.3

| x - 2 | > 3
Is this an "and"  or an "or" problem?

• and
• or

Tags

CCSS.HSA.REI.B.3

| x - 2 | > 3
Is this an "and"  or an "or" problem?

• and
• or

| -8x | < 8

What is the correct first step?

• separate into two inequalities with an "and"

• separate into two inequalities with an "or"

• divide both sides by -8

• add 8 to both sides

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.3

What is the correct first step?

• divide by 10
• multiply by 10
• make it two inequalities with an "or"
• make it two inequalities with and "and

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.CED.A.3

CCSS.HSA.REI.B.3

What is the first step?

• Get the absolute value alone by dividing both sides by 5
• Drop the absolute value bars and add 7 and 5 together
• Get the absolute value alone by subtracting 5 from both sides

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.A.1

CCSS.HSA.REI.B.3

| k - 3 | < -1

• No Solution
• All Real Numbers
• 2 < k < 4
• k < 2  or  k > 4

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.CED.A.3

CCSS.HSA.REI.B.3

| n + 2 | - 3 ≥ -6

• No Solution
• All Real Numbers
• n ≤ -5  or  n ≥ 1
• -5 ≤ n ≤ 1

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.CED.A.3

CCSS.HSA.REI.B.3

Solve:
 |x + 3| > 8

• x > 5 or x < -11
• x > 5
• all real numbers
• no solution

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.3