A Wide Absolute Value

Take |3x - 6| <= 9. The sign is "less than or equal to", so the absolute value becomes a chain. Then do two steps on all three parts.

-9 <= 3x - 6 <= 9

-3 <= 3x <= 15

-1 <= x <= 5

The condition says that 3x - 6 is within 9 of zero. For x itself, this means within 3 of 2, so the solution is the segment from -1 to 5.

First get the absolute value bars alone on one side. Here they already are. Then look at the sign. A "less than" gives a chain, and a "greater than" gives two cases joined by "or". After the split, the steps are the same as for any chain or any pair of inequalities.