9514 1404 393
Answer:
1 < 15 -2a < 7
Explanation:
There are a couple of ways you can do this.
1) Put the minimum and maximum values of a into the expression to see what its corresponding values are:
15-2a for a=4:
15-2(4) = 7
15-2a for a=7:
15-2(7) = 1
Then ...
1 < 15-2a < 7
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2) Solve for a in terms of the value of 15-2a, then impose the limits on a.
x = 15 -2a
2a = 15 -x
a = (15 -x)/2
Now, impose the given limits:
4 < (15 -x)/2 < 7
8 < 15 -x < 14 . . . multiply by 2
-7 < -x < -1 . . . . . . subtract 15
7 > x > 1 . . . . . . . . multiply by -1
1 < 15-2a < 7 . . . . . use x=15-2a
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The vertical extent of the attached graph is the range of possible values of 15-2a. It goes from 1 to 7.