17) We have two inequalities and we have to find the interval for x that is the solution set.
We can start with 3x<6:
[tex]\begin{gathered} 3x<6 \\ x<\frac{6}{3} \\ x<2 \end{gathered}[/tex]
Now, we solve the other inequality as:
[tex]\begin{gathered} 2(5-x)\leq x-2 \\ 10-2x\leq x-2 \\ 10+2\leq x+2x \\ 12\leq3x \\ \frac{12}{3}\leq x \\ 4\le x \\ x\geq4 \end{gathered}[/tex]
Then,the solution set would be the intersection of the sets x < 2 and x ≥ 4.
As there is not value of x that belong to both sets, we can conclude that this inequalities combined have no solution.
Answer: No solution
