Question

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

Answer 1

Answer:

Whenever  $a\leq 5$.

Step-by-step 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!

Answer 2

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