Question

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

Answer 1

`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))))`