Question

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

Answer 1

Answer:

Any negative number and 0 works for the expression.

Step-by-step 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

$|6| = -(6)\\6 \neq -6$

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

$|9| = -(9)\\9 \neq -9$

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!

Answer 2

Answer:

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

Step-by-step explanation:

Recall that absolute values are always 0 or positive.  

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