Question

For the compound inequalities below (5-7), determine whether the inequality results in an overlapping region or a combined region. Then determine whether the circles are open are closed. Finally, graph the compound inequality. Simplify if needed. x-1>_5 and 2x<14

Answer 1

The inequalities are:

`x-1\ge5\text{ and }2x<14`

So, we need to solve for x on both inequalities as:

`\begin{gathered} x-1\ge5 \\ x-1+1\ge5+1 \\ x\ge6 \end{gathered}`
`\begin{gathered} 2x<14 \\ (2x)/(2)<(14)/(2) \\ x<7 \end{gathered}`

Now, we can model the inequalities as:

So, the region that results is an overlapping region and it is written as:

6 ≤ x < 7

So, the lower limit 6 is closed and the upper limit 7 is open.

Answer: The region is overlaping and it is 6 ≤ x < 7