SOLUTION: Find a and b. If -3 < x < 0, then a < 1/(x + 4)

SOLUTION: Find a and b. If -3 < x < 0, then a < 1/(x + 4) < b

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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