4338f02e-64fb-43cf-88ae-906aaaa9b492.html

<p>Refer to the work students have done in the last activity. Discuss with students how they made decisions about the solution region and boundary line for the given inequalities, and about the inequality symbol for the given graphs. Ask questions such as:</p>
<ul>
  <li>"Once you knew where the boundary line is, how did you decide which side of the line represents the solution region?"</li>
  <li>"How did you decide whether the boundary line should be solid or dashed?"</li>
  <li>"When you have the graph showing the solution region, how did you determine the inequality symbol to use?"</li>
</ul>
<p>Some students might incorrectly conclude that an inequality with a \(&lt;\) symbol will be shaded below the boundary line and that an inequality with a \(&gt;\) symbol will be shaded above it. Any inequality in the first question can be used to show that this is not the case.</p>
<p>Take \( x&minus;y&lt;5 \) for example. We're looking for coordinate pairs that have a value of less than 5 when \(y\) is subtracted from \(x\). Let's see if \((0,0)\) meets this condition: \(0&minus;0&lt;5\) gives \(0&lt;5\), which is a true statement. This means that \((0,0)\), which is above the graph of \( x&minus;y=5 \), is in the solution region. If we test a point below the line, say, \((10,-10)\), we would see that \(x&minus;y\) is greater than 5, not less than 5. This means that the region below the line is for non-solutions.</p>
<p>Emphasize that we cannot assume that the \(&lt;\) or \(&le;\) symbol means shading below a line. It is important to test points on either side of the line to see if the pair of values make the inequality true, or to reason carefully about the inequality statement and think about pairs of values that would satisfy the inequality.</p>