Question

For what value or values of b is it true that |b| = -b

Answer 1

Answer: b = 0 or anything negative (like b = -2)

So any value of b such that $b \le 0$

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Explanation:

|b| is the distance from b on the number line to 0

The distance is never negative as negative distance does not make sense.

If b was some positive number, then |b| = b. For instance, |7| = 7. This shows 7 is seven units away from 0 on the number line.

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If b is negative or zero, then |b| = -b. Why? Because the result of |b| is the opposite of whatever negative b value you put in. For example, b = -2 leads to

|b| = |-2| = 2

while

-b = -(b) = -(-2) = 2

The two negatives cancel each other out to get a positive result.

This shows, |-2| = -(-2) = 2

Meaning that the location -2 is two units away from 0 on the number line.

Answer 2

Answer:

b =0

Step-by-step explanation:

The only value where  |b| = -b  is when b=0

|0| = -0

0 = 0

Absolute value means non- negative

non-negative = negative

This is only true when we equal zero