A1H Absolute Value Inequalities

• no solution
• -6 ≤ r ≥ 8
• 6 > r > -8
• -6 < r < 8

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.CED.A.3

CCSS.HSA.REI.B.3

• no solution
• x > 2 or x < -22
• -22 < x < 2
• all real numbers

Tags

CCSS.HSA.REI.B.3

• r > 11/4 or r < 9/4
• r > 5 or r ≤ 0
• r > 5 or r < 0
• r < -5 or r > 0

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.CED.A.3

CCSS.HSA.REI.B.3

• all real numbers
• no solution
• 0 < v < 6⁄7
• 0 ≤ v ≤ 6/7

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.CED.A.3

CCSS.HSA.REI.B.3

• no solution
• -6 < x < 26
• x < -6 or x > 26
• all real numbers

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.CED.A.3

CCSS.HSA.REI.B.3

• no solution
• all real numbers 
• -2 ≤ n ≤ 16
• n ≤ -2 or n ≥ 16

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.CED.A.3

CCSS.HSA.REI.B.3

The radius of the gears produced at a factory must be 6 inches in length with a tolerance of 0.1 inches. The gears with radius beyond the tolerated lengths will be thrown away. If x is the length of the radius, which of the following inequalities can be used to assess which gears are eligible to keep?

• |x – 6| ≤ 0.1

• |x – 6| ≥ 0.1

• |x – 0.1| ≤ 6

• |x – 0.1| ≥ 6

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.CED.A.3

CCSS.HSA.REI.B.3

The average temperature in Las Vegas in July is 110 degrees.  If the temperature can vary up to 10 degrees, which equation represents this situation?

• | x - 10 | < 110
• | 110 - x | < 10
• | x - 110 | < 10
• | 10 - x | < 110

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.CED.A.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

Solve.
|c + 4| < 5

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

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.3