Question

1. explain the error in graphing the inequality. ( x - 2 > 3 ) or ( x + 8 < -2 ) ( x > 5 ) or ( x < -10 ) number line from -15 to 10 with open circles at -10 and 5

Explanation:

Step1: Solve \(x + 8 < -2\)

To solve \(x + 8 < -2\), subtract 8 from both sides: \(x + 8 - 8 < -2 - 8\), so \(x < -10\).

Step2: Analyze the graph for \(x < -10\)

For the inequality \(x < -10\), the solution set includes all numbers less than -10. On a number line, this should be represented by an open circle at -10 (since -10 is not included) and an arrow pointing to the left (towards more negative numbers). But in the given graph, the open circle for \(x < -10\) is at 10, which is incorrect. It should be at -10. Also, for \(x>5\), the open circle is at 5 (correct), but the error is mainly in the placement of the open circle for \(x < -10\) (it's at 10 instead of -10) and the direction or placement related to \(x < -10\) is misrepresented. Another way: when solving \(x + 8 < -2\), we get \(x < -10\), so the critical point is -10, not 10. The graph has an open circle at 10 for the \(x < -10\) part, which is wrong. It should be at -10 with an arrow to the left.

Answer:

The error is in the graphing of \(x + 8 < -2\) (which simplifies to \(x < -10\)). The open circle for \(x < -10\) is placed at 10 (incorrect); it should be placed at -10 (with an arrow pointing to the left to represent all values less than -10). Also, the representation for \(x < -10\) is mispositioned (using 10 instead of -10 as the critical point).