Determine Algebraically Whether the Following Function Is One-To-One $$| x - 5 | , \quad x \leq 5$$

Determine algebraically whether the following function is one-to-one.
$$| x - 5 | , \quad x \leq 5$$

A)
$$\begin{aligned}| a - 5 | & = | b - 5 | \\5 - a & = 5 - b \quad ; \text { one-to-one } \\- a & = - b \quad \\a & = b\end{aligned}$$
B)
$$\begin{aligned}| a - 5 | & = | b - 5 | \\| a | - 5 & = | b | - 5 \\| a | & = | b | \\a & = b\end{aligned}$$
C)
$$\begin{aligned}| a - 5 | & = | b - 5 | \\a + 5 & = 5 - b \quad ; \text { not one-to-one } \\a & = - b\end{aligned}$$
D)
$$\begin{aligned}| a - 5 | & = | b - 5 | \\| - 5 | - a & = | - 5 | + b ; \text { not one-to-one } \\- a & = b\end{aligned}$$
E)
$$\begin{aligned}| a - 5 | & = | b - 5 | \\| - 5 | - a & = | - 5 | - b \\- a & = - b \\a & = b\end{aligned}$$