Rewriting $|x-10|+|y-5|\leq 7$ so that absolute values disappear - Algebra

Question

Equation 1: $|x-10|+|y-5|\leq 7$

I want to rewrite this equation into equations that do not have the absolute value.

$|A|\leq b$ can be written as

$A \leq b$

$A \geq -b$

I want to apply the same technique but there are two absolute values in the equation 1. I have:

$(x-10)+(y-5)\leq 7$
$(x-10)+(y-5)\geq -7$

Are the above equations correct? Also, do I miss some other equations other than the two above?

Answer 1

$$|x-10|+|y-5|\leq 7 $$can rewrite as :$$\left\{\begin{matrix} (x-10)+(y-5) \leq 7& x \geq 10 & y \geq 5\\ (x-10)-(y-5) \leq 7& x \geq 10 & y \leq 5 \\ -(x-10)+(y-5) \leq 7& x \leq 10 & y \geq 5 \\ -(x-10)-(y-5) \leq 7& x \leq 10 & y \leq 5 \end{matrix}\right.$$