Solve #abs(a-5)=5-a#?

1 Answer

Answer:

#a<=5#

Explanation:

We have:

#abs(a-5)=5-a#

When solving absolute value questions, we need to consider both positive and negative values within the absolute value brackets (consider that with #absx=3#, #x# could be 3 and it could also be #-3#).

Positive

#a-5=5-a#

#2a=10#

#a=5#

Negative

#-(a-5)=5-a#

#-a+5=5-a#

In this case there is an infinite number of solutions, which means the two equations are equivalent.

And so the final solution starts at #a=5# and then continues towards #-oo#. We can write this as

#color(blue)(ul(bar(abs(color(black)(a<=5))))#