Question

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Explanation:

Step1: Expand the right side

First, we expand the right - hand side of the inequality \(3x<3(x - 6)\). Using the distributive property \(a(b + c)=ab+ac\) (here \(a = 3\), \(b=x\), \(c=-6\)), we get \(3x<3x-18\).

Step2: Subtract \(3x\) from both sides

Subtract \(3x\) from both sides of the inequality \(3x<3x - 18\). We have \(3x-3x<3x - 18-3x\). Simplifying both sides, the left - hand side is \(0\) and the right - hand side is \(- 18\). So we obtain the inequality \(0<-18\). But \(0\) is not less than \(-18\), which means there are no real numbers \(x\) that satisfy the original inequality.

Answer:

For the first part, the correct choice is B. The solution set is \(\varnothing\).

For the second part (the graph of the solution set), the correct choice is D. The solution set is \(\varnothing\).