Question

1. consider the inequalities $xleq7$, $x > -\frac{11}{2}$, $xleq6$ and $x > -\frac{3}{2}$. which one of the following graphs satisfies all four inequalities?

Explanation:

Step1: Analyze the inequalities

We have \(x\leq7\), \(x >-\frac{11}{2}=- 5.5\), \(x\leq6\) and \(x>-\frac{3}{2}=-1.5\). The intersection of these inequalities is \(-1.5 < x\leq6\).

Step2: Check graph - features

A closed - circle is used for \(\leq\) or \(\geq\) and an open - circle is used for \(>\) or \(<\). For \(x > - 1.5\), there should be an open - circle at \(x=-1.5\) and for \(x\leq6\), there should be a closed - circle at \(x = 6\), and the line should be between these two points.

Answer:

The graph with an open - circle at \(x=-1.5\), a closed - circle at \(x = 6\) and the line segment connecting them. (Since no options are labeled, a general description is provided. If options were labeled, we would identify the correct option label).