Question

For what values of a the following expressions are true: |a|=−a

Answer 1

|a|=−a is true only if a is negative or zero

Explanation:

Recall that absolute values are always 0 or positive.

|a|=−a is true only if a is negative or zero.

Answer 2

Any negative number and 0 works for the expression.

Explanation:

Looking at this type of equation, we know that either EVERY negative number and 0 or EVERY positive number and 0 will work for this equation, since nothing is being added and we're just working with absolutes/negatives.

Let's try a random positive number in the expression

`|6| = -(6)\\6 \\eq -6`

So this positive number doesn't work, let's just test with another one.

`|9| = -(9)\\9 \\eq -9`

So we know that positive numbers won't work with this expression.

Let's test 0 quickly, just to make sure.

`|0| = -0\\0 = 0`

So 0 works.

Let's try a few negative numbers now.

`|-5| = -(-5)\\5 = 5`

So yes, this does work. Let's try one more negative number.

`|-120| = -(-120)\\120 = 120`

This works. So, every negative number and 0 work with this equation.

Hope this helped!