What is the number line interval for (0\le \frac{x-4}{3}<2)?

Correct answer: ([4,10))

The direct answer is option A: [4,10). Begin with 0≤(x-4)/3<2. Multiply every part by positive 3; the signs remain unchanged: 0≤x-4<6. Add 4 to all parts: 4≤x<10. Thus 4 is included and receives a closed point or square bracket, while 10 is excluded and receives an open point or round bracket. Option A is exactly [4,10). Option B incorrectly excludes 4 and includes 10, reversing both endpoint rules. Option C gives the bounds from the unsolved middle expression rather than the x-values. Option D represents values outside the interval and is unrelated to the solution set. A useful check is to test x=4: it gives 0, so it must be included; x=10 gives 2, but the upper sign is strict, so it must be excluded.