Question

Solve the following continued inequalities. Use both a line graph and interval notation to write each solution set.−1 <1/3y+5 <3

Answer 1

Answer:

The solution to the inequality is:

`-18A sketch of the graph is shown below:<p></p>Explanation:<p>Given </p>[tex]-1<(1)/(3)y+5<3`

Separarating this into two inequalities, we have:

`\begin{gathered} -1<(1)/(3)y+5 \\ \\ \\ (1)/(3)y+5<3 \end{gathered}`

Solving the inequalities one after the other:

`\begin{gathered} -1<(1)/(3)y+5 \\ \\ -1-5<(1)/(3)y \\ \\ -6<(1)/(3)y \\ \\ -6*3-18 \end{gathered}`

For the other part:

`\begin{gathered} (1)/(3)y+5<3 \\ \\ (1)/(3)y<3-5 \\ \\ (1)/(3)y<-2 \\ \\ y<-2*3=-6 \end{gathered}`

Therefore, the solution to the inequality is:

[tex]-18