Question

Solve the compound Inequalities, graph thebsolutions and write thebsolutions in interval notation.

Answer 1

Given the inequalities:

`4x-3\le13\text{ and -}x-5<-5`

First, we solve each of the inequality:

`\begin{gathered} 4x-3\le13\text{ and -}x-5<-5 \\ 4x\le13+3\text{ and }-5+50 \end{gathered}`

The solution in interval notation is:

`(-\infty,4\rbrack\cap(0,\infty)=(0,4\rbrack`

Next, we plot the graph.

Note that since we have the word 'AND', the graph will show only the region satisfied by the two inequalities.