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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

Respuesta :

The inequalities are:

[tex]x-1\ge5\text{ and }2x<14[/tex]

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

[tex]\begin{gathered} x-1\ge5 \\ x-1+1\ge5+1 \\ x\ge6 \end{gathered}[/tex][tex]\begin{gathered} 2x<14 \\ \frac{2x}{2}<\frac{14}{2} \\ x<7 \end{gathered}[/tex]

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

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