Question 1199343: Find a and b.
If -3 < x < 0, then a < 1/(x + 4) < b
Answer by math_tutor2020(3817)   (Show Source):
You can put this solution on YOUR website!
Add four to all sides of the 1st inequality
-3 < x < 0
-3+4 < x+4 < 0+4
1 < x+4 < 4
The inequality signs stay the same for now.
Then apply the reciprocal to all three sides.
This flips the direction of the inequality signs.
It's like saying how 2 > 1/3 flips to 1/2 < 3.
So,
1 < x+4 < 4
1/1 > 1/(x+4) > 1/4
1 > 1/(x+4) > 1/4
Now let's go from the form p > q > r to r < q < p
1 > 1/(x+4) > 1/4
1/4 < 1/(x+4) < 1
In other words, swap the 1st and last sides so that the "greater than" signs become "less than" signs.
Compare that to the form
a < 1/(x+4) < b
to find that
a = 1/4
b = 1
which are the final answers.
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