Absolute Value Inequalities

What's a way to define absolute value?

• The value of a number
• The opposite of a number
• The distance of a number from zero
• The multiplicative inverse of a number

Tags

CCSS.6.NS.C.7C

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

Solve.
|c + 4| < 5

• x < -9 or x > 1
• -9 < x < 1
• x < 9 or x > -1
• -1 < x < 9

Solve:
|x + 4| - 8 > 2

• x > 6 and x < 10
• x > 6 or x < -14
• all real numbers
• no solution

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.3

Solve.
|y - 4| ≥ 8

• y ≤ -4 or y ≥ 12
• -4 ≤ y ≤ -12
• y ≤ 4 or y ≥ -12
• -12 ≤ x ≤ 4

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.CED.A.3

CCSS.HSA.REI.B.3

Solve the absolute Value inequality and graph. 

• A
• B
• C
• D

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.3

Write an inequality for Graph 3.

• x ≤ -2 AND x > 5
• x ≤ -2 OR x > 5
• x ≥ -2 OR x < 5
• -2 ≤ x < 5

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.CED.A.3

Write an inequality for Graph 4.

• -2 < x < 5
• x < -2 or x > 5
• x ≥ -2 OR x < 5
• -2 ≤ x ≤ 5

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.CED.A.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

• v>5 or v<-5
• v≥5 or v≤-5
• v>-5 or v<5
• all real numbers

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.CED.A.3

CCSS.HSA.REI.B.3