Question

solve the following and graph the solutions: - 3x + 7 > - 1 or - 3x + 7 < 1 x < \frac{8}{3} or x > 2 x < \frac{8}{3} or x > 2 x < \frac{8}{3} or x > 2 x < \frac{8}{3} or x > 2

Explanation:

Step1: Analyze the inequality \(x < \frac{8}{3}\) or \(x>2\)

For \(x < \frac{8}{3}\approx2.67\), we have all real - numbers less than \(\frac{8}{3}\). For \(x > 2\), we have all real - numbers greater than \(2\).

Step2: Graph the solution on the number line

When graphing \(x>2\), we use an open circle at \(x = 2\) (since \(x
eq2\)) and draw an arrow to the right. When graphing \(x<\frac{8}{3}\), we use an open circle at \(x=\frac{8}{3}\) (since \(x
eq\frac{8}{3}\)) and draw an arrow to the left. The union of these two sets means that the graph will have two separate parts: one to the left of \(\frac{8}{3}\) (excluding \(\frac{8}{3}\)) and one to the right of \(2\) (excluding \(2\)).

Answer:

The first option (the one with two open - circle points at \(2\) and \(\frac{8}{3}\) and arrows going in opposite directions) is the correct graph.