Question

For what values of a the following expressions are true: |a−5|=5−a

Answer 1

It’s 0 I think but I am not sure I might be wrong but oh well

Answer 2

Whenever
`a\leq 5`.

Explanation:

We can play around with some numbers and develop some rules for this equation.

Note that the number 5 and -5 are used here, so let's try using 5 as a.

`|5-5| = 5-5\\|0| = 0\\0 = 0`

So 5 works. Let's try a random number like 3.

`|3-5| = 5-3\\|-2| = 2\\2 = 2`

Okay, with this info we know that we might be able to develop one rule that
`a<5`. Just to test, let's try 0, -3, and -5.

`|0-5| = 5-0\\|-5| = 5\\5 = 5`

Zero works.

`|-3 - 5| = 5-(-3)\\|-8| = 8\\8 = 8`

-3 works.

`|-5 -5| = 5-(-5)\\|-10| = 10\\10 = 10`

-5 works. Now, this might stop here making the equation
`-5 \geq a \leq 5`, so let's test a number outside of -5 - say -20.

`|-20 - 5| = 5-(-20)\\|-25| = 25\\25 = 25`

Yes! This works, so a works for this equation as long as
`a \leq 5`.

Hope this helped!