S = {x ∈ R : 3≤x≤12}
1) To solve a compound inequality, we must do it one by one.
Let's start with
1.1) 0≤1/3x -1
1≤1/3x-1+1
1≤1/3x Multiplying both sides by 3
3≤x Flipping it
x≥3
1.2) 1/3x -1≤3
1/3x -1+1≤3+1
1/3x≤4
x≤12
2) Let's find out the solution, by graphing on three lines. The first one for the first solution, the second for the second inequality's solution, and the third for the intersection of the above:
So the Solution set is S = {x ∈ R : 3≤x≤12}
