Question 312972
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<b>Step 1:</b>  Choose either inequality.  Change the relationship symbol to "=".  Graph the resulting line, but do it with a dashed or broken line.  The dashed or broken line is used because your inequality symbols are exclusive of equals.  If your symbols had been *[tex \LARGE \leq] or *[tex \LARGE \geq], then you would use a solid line.

<b>Step 2:</b>  Pick any point on the coordinate plane that <b><i>does not</i></b> lie on the line you just graphed. If the line does not pass through the origin, *[tex \Large (0,0)] then the origin is an excellent choice for this step.  If the line does pass through the origin, select a point other than the origin -- I recommend a point that has small integer coordinates.

<b>Step 3:</b>  Substitute the values of the coordinates of the point chosen in Step 2 for the corresponding variables in the inequality you started with in Step 1.

<b>Step 4:</b>  Do the appropriate arithmetic to determine whether the substitution created a true statement or not.  If you created a true statement, shade in the side of the line <b><i>containing</i></b> the point selected in Step 2.  If you created a false statement, shade in the side of the line that <b><i>does not contain</i></b> the selected point.

<b>Step 5:</b>  Repeat steps 1 through 4 for the other inequality.  The solution set will be the region where the two shaded areas overlap.  If the two shaded areas do not overlap at all, the solution set is the empty set.  Note that points on the dashed lines, in this case where you do not have *[tex \LARGE \leq] or *[tex \LARGE \geq] relationships, are NOT included in the solution set.

John
*[tex \LARGE e^{i\pi} + 1 = 0]
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