Absolute Value Tolerance

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

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

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

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

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

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

Solve:
 |x + 3| > 8

• x > 5 or x < -11

• x > 5

• all real numbers

• no solution

Solve.
|c + 4| < 5

• x < -9 or x > 1

• -9 < x < 1

• x < 9 or x > -1

• -1 < x < 9

• - 1/2 ≤ z ≤ 5/2
• 1/2 ≤ z ≤ 5/2
• z ≥ 1/2 or z ≤ 5/2
• z ≤ 1/2 or z ≥ 5/2

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