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