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Knowing that 6 < x < 7 and 10 < y < 12, find the possible values of, y-x

User Rida Rezzag
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2 Answers

14 votes
14 votes

Answer:

3 < y-x < 6

Step-by-step explanation

just look above... yeah there it is.

User Rudrik
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14 votes
14 votes

Answer: 3 < y-x < 6

The value of y-x is between 3 and 6, excluding both endpoints.

========================================================

Step-by-step explanation:

10 < y < 12 breaks down into 10 < y and y < 12

Subtract x from both sides in 10 < y

10 < y

10-x < y-x

Then plug in the upper bound of x, which is 7

Do so for only the first value of x

10-7 < y - x

3 < y-x

This establishes the lower bound of y-x

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Now focus on y < 12

Subtract x from both sides

y < 12

y-x < 12-x

And plug in the lower bound of x into the second copy of x

y-x < 12-6

y-x < 6

This is the upper bound of y-x

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For the expression y-x, we have:

  • lower bound = 3
  • upper bound = 6

Therefore, 3 < y-x < 6

The value of y-x is between 3 and 6, excluding both endpoints.

User Tawfeeq Amro
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