Recall the definition of absolute value.
[tex]|x| = \begin{cases} x & \text{if } x \ge 0 \\ -x & \text{if } x < 0 \end{cases}[/tex]
Now,
[tex]x<1 \implies x-9 \le -8 < 0 \implies |x-9| = -(x-9) = 9 - x[/tex]
and
[tex]x<1 \implies x-6 \le -6 < 0 \implies |x-6| = -(x-6) = 6 - x[/tex]
so that
[tex]|x-9| + |x-6| = (9-x) + (6 - x) = \boxed{15 - 2x}[/tex]
