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The dark purple region on the number line above is shown in its entirety. This region is delineated by which of the following inequalities?
  • a)
    10 < |x + 10| < 80
  • b)
    10 < |x – 100| < 80
  • c)
    |x – 20| < 70
  • d)
    |x – 20| < | x – 90|
  • e)
    |x – 55| < 35
Correct answer is option 'E'. Can you explain this answer?
Verified Answer
The dark purple region on the number line above is shown in its entire...
Step one: find the midpoint of the region.
The midpoint, halfway between and 20 and 90, is 55.
In other words, 20 and 90 have the same distance from 55, a distance of 35.
These endpoints are not included, but the region includes all the points that have a distance from from x = 55 that is less than 35.
Translating that into math, we get the following:
|x – 55| < 35
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The dark purple region on the number line above is shown in its entirety. This region is delineated by which of the following inequalities?a)10 < |x + 10| < 80b)10 < |x – 100| < 80c)|x – 20| < 70d)|x – 20| < | x – 90|e)|x – 55| < 35Correct answer is option 'E'. Can you explain this answer?
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