need algebra help stat!?

Question

My daughter really needs help solving this algebra question, it states, solve the inequality:

|4-b| <4-b

Please help!!!! Thanks

Answer 1

For absolute values in inequalities, you're going to have two cases:

1) |x| < a (for some positive value a).

In this case, the inequality converts to x < a AND x > -a, or, quite simply, -a < x < a.

2) |x| > a (for some positive value a).

In this case, it is an OR; that is, this translates into
x > a OR x < -a.

Obviously, in our case, we have the less than sign, so we have the AND.

|4 - b| < 4 - b

By the definition above, this becomes

4 - b < 4 - b AND 4 - b > -(4 - b)

Solving the first inequality, we get

4 - b < 4 - b {adding b to both sides,}
4 < 4, which is a false statement.

Therefore, the inequality has no solution.

Answer 2

The absolute value of 4 - b is less that 4 - b. The absolute value cannot be less than the number. The opposite is possible. But this value of b is an empty set..

Answer 3

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Answer 4

|4-b|< 4-b
This is never true.
The |4-b| = or > 4-b
This can be shown more easily by graphing |4-x| and 4-x on the same coordinate system. You will see that |4-x| = 4-x for x = or < 4 and is > b-4 for all x >4.

Answer 5

use the law of absolute values in her book. there will be an example.

Answer 6

I do not get it. That problem does not look like it makes sense.