SOLUTION
Given the question in the image, the following are the solution steps
Step 1: Write out the inequalities
[tex]-5(y-4)\leq30\text{ or }18+y<20[/tex]
Step 2: Solve for y by making y the subject of the formula
[tex]\begin{gathered} -5y+20\le30\text{ or }18+y<20 \\ -5y\le30-20\text{ or }y<20-18 \\ -5y\le10\text{ or }y<2 \\ -y\le2\text{ or }y<2 \\ y\ge-2\text{ or }y<2 \end{gathered}[/tex]
Step 3: Combine the intervals
[tex]\begin{gathered} y\ge-2\text{ or }y<2 \\ y\ge-2\Rightarrow(-2,\infty) \\ y<2\Rightarrow(-\infty,2) \\ \text{ }-5(y-4)\leq30\text{ or }18+y<20\text{ means we find the union of the two intervals} \\ -5(y-4)\leq30\text{ or }18+y<20\Rightarrow(-\infty,\infty) \end{gathered}[/tex]
This means that the interval notation will be:
[tex](-\infty,\infty)[/tex]
