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Can someone help me with this! And please explain the steps so I can knoe for next time

Can someone help me with this! And please explain the steps so I can knoe for next-example-1
User Hlidotbe
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1 Answer

4 votes

Our main objective is to describe the shaded region.

To answer this, first we need to determine the equation of the lines that bounds the shaded region.

Here we have a line at x =2 and x = 4

Notice that the shaded region is on the right of x = 2 ( therefore we can say that the shaded region is greater than x = 2 ) and on the left of x = 4 ( we can also say that the shaded region is less than x = 4

Another important thing to notice is the line that bounds the region, if it is a broken line or a solid line. If it's a broken line, it means that we dont have to include its value/expression. Instead of x is greater than or equal to 2 ( we will not include 2 since x = 2 is a broken line), we will only put it as x > 2. The same goes for the boundary at x = 4 ( being a broken line ) , it must be x < 4 only.

To further illustrate the difference, if the lines in the figure are solid lines then our answer will be:


\begin{gathered} x\ge2 \\ x\leq4 \end{gathered}

But since it's a broken line , then our answer is only:


\begin{gathered} x>2 \\ x<4 \end{gathered}

There will be times that the problem is not a vertical or horizontal line, but a slanting line. In those cases you have to solve for the equation of the lines and describe the shaded region accordingly using the concept of the broken/solid lines and > or <. If the shaded region is above or to the right of a line then use "greater than" or "greater than or equal". If the shaded region is below or to the left of the line then use " less than" or "less than or equal" as the case may be.

User MadaManu
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