Question

17)Solve each equation or inequality. Write solutions to inequalities in interval notation. If no solutions exist, write no solution.

Answer 1

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:

`\begin{gathered} 3x<6 \\ x<(6)/(3) \\ x<2 \end{gathered}`

Now, we solve the other inequality as:

`\begin{gathered} 2(5-x)\leq x-2 \\ 10-2x\leq x-2 \\ 10+2\leq x+2x \\ 12\leq3x \\ (12)/(3)\leq x \\ 4\le x \\ x\geq4 \end{gathered}`

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