1. Solve $|-x| = 3,4$. Since $|-x| = |x|$, the equation $|x| = 3$ has solutions $x = 3$ and $x = -3$. Similarly, $|x| = 4$ has solutions $x = 4$ and $x = -4$. 2. Solve $|-x| = 2,1$. Again, $|x| = 2$ gives $x = 2$ and $x = -2$, and $|x| = 1$ gives $x = 1$ and $x = -1$. 3. Solve $|5 - x| = 5$. Set $5 - x = 5$ or $5 - x = -5$. From $5 - x = 5$, we get $x = 0$. From $5 - x = -5$, we get $x = 10$. 4. Solve $|3 - x| = 8$. Set $3 - x = 8$ or $3 - x = -8$. From $3 - x = 8$, $x = -5$. From $3 - x = -8$, $x = 11$. 5. Solve $|x - 7| = 1$. Set $x - 7 = 1$ or $x - 7 = -1$. From $x - 7 = 1$, $x = 8$. From $x - 7 = -1$, $x = 6$. 6. Solve $|5 - x| = 2$. Set $5 - x = 2$ or $5 - x = -2$. From $5 - x = 2$, $x = 3$. From $5 - x = -2$, $x = 7$. Final answers: 1) $x = \pm 3, \pm 4$ 2) $x = \pm 1, \pm 2$ 3) $x = 0, 10$ 4) $x = -5, 11$ 5) $x = 6, 8$ 6) $x = 3, 7$