Question

Solve the second inequality and express your answer in interval notation. Use decimal form for numerical values.

Answer 1

Given the question in the image, the following are the solution steps

Step 1: Write out the inequalities

`-5(y-4)\leq30\text{ or }18+y<20`

Step 2: Solve for y by making y the subject of the formula

`\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}`

Step 3: Combine the intervals

`\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}`

This means that the interval notation will be:

`(-\infty,\infty)`