Late 2.2 Solve absolute Value inequalities

solve

|b − 8|+10 > 22

• −4 < b < 20

• b <−4 or b > 20

• 20 < b < −4

• b = −4 or b = 20

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Girls selected for a dance team should be 165 cm in height but it can vary by 5 cm. Which of the following inequalities can be used to assess which girls' heights are tolerable?

(h is the height of the girl) .

• |h – 5| ≤ 165

• |h – 5| ≥ 165

• |h – 165| ≤ 5

• |h – 165| ≥ 5

The street built in the city must be 25 feet in width with a tolerance of 0.5 feet. Streets that are not within the tolerated widths must be repaired. Which of the following inequalities can be used to assess which streets are within tolerance? (W is the width of the street) .

• |W – 0.5| ≥ 25

• |W – 0.5| ≤ 25

• |W – 25| ≥ 0.5

• |W – 25| ≤ 0.5

Solve:

3| 2x + 7| − 7 < −4

• x < −3 and x > −5/3

• x < −3 and x > −4

• all real numbers

• no solution

Solve:
3 | 2x + 7| + 7 < 4

• x < -3 and x > -5/3
• x < -3 and x > -4
• all real numbers
• no solution

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.3

Solve:

|x + 4| − 8 > 2

• x > 6 and x < 10

• x > 6 or x < -14

• all real numbers

• no solution

A company makes boxes of crackers that should weigh 213g. A quality control inspector randomly selects boxes to weigh. Any box that varies from the weight by more than 5g is sent back. What is an equation that shows the range of allowable weights for a box of crackers and what is the range?

• |w - 213| ≤ 5,

  208 ≤ w ≤ 218

• |w - 213| ≤ 5,

  0 ≤ w ≤ 10

• |w - 5| ≤ 213,

  208 ≤ w ≤ 218

• |w - 5| ≤ 213,

  0 ≤ w ≤ 10

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. Which of the following inequalities can be used to assess which gears are eligible? (x is the length of the radius)

• |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