SOLUTION: Solve |b-7|< 6 a. 1>b>13 b. b>1 c. 1< b<13

Question 1190064: Solve |b-7|< 6
a. 1>b>13
b. b>1
c. 1< b<13
Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!

The handy rule to memorize is
|x| < k is the same as -k < x < k
where k is some positive number
If k was negative, then |x| < k has no solutions. Why? Because |x| itself is never negative, so there's no way |x| is smaller than any negative number.

Some examples

|x| < 5 becomes -5 < x < 5
|3y-1| < 10 is the same as -10 < 3y-1 < 10
|w+4| < 7 turns into -7 < w+4 < 7
|10n-22| < -55 has no solutions

With all that in mind, let's solve this current inequality
|b-7| < 6
-6 < b-7 < 6 ... use the rule mentioned above
-6+7 < b-7+7 < 6+7 .... adding 7 to all sides
1 < b+0 < 13
1 < b < 13

The value b is some number between 1 and 13, excluding both endpoints.

The graph will have open holes at 1 and 13 on the number line.
Then you shade between those open holes. This visually describes the interval 1 < b < 13.

Answer: Choice C. 1 < b < 13

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