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

$a \le 5$

#### Explanation:

We have:

$\left\mid a - 5 \right\mid = 5 - a$

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

Positive

$a - 5 = 5 - a$

$2 a = 10$

$a = 5$

Negative

$- \left(a - 5\right) = 5 - a$

$- a + 5 = 5 - a$

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 $- \infty$. We can write this as

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