Question

in set-builder notation, the solution set is \\{x \mid x > -\frac{25}{7}\\}.

part 2 of 3

in interval notation, the solution set is \left(-\frac{25}{7}, \infty\
ight).

part: 2 / 3

part 3 of 3

graph the solution set on the number line.

number line image with -4, -3, -2, -1, 0, 1, 2, 3, 4

Explanation:

Step1: Convert \(-\frac{25}{7}\) to decimal

\(-\frac{25}{7}\approx - 3.57\) (since \(25\div7\approx3.57\))

Step2: Locate the point on the number line

Find the position of \(-\frac{25}{7}\) (or approximately \(-3.57\)) on the number line. Since the inequality is \(x>-\frac{25}{7}\), we use an open circle at \(-\frac{25}{7}\) (because the inequality is strict, \(>\) not \(\geq\)) and draw an arrow to the right (indicating all numbers greater than \(-\frac{25}{7}\)).

To graph:

1. Mark the point \(-\frac{25}{7}\approx - 3.57\) on the number line.
2. Draw an open circle at this point (because \(x\) is strictly greater than \(-\frac{25}{7}\), not equal to it).
3. Draw a ray (line with an arrow) starting from the open circle and going to the right (towards positive infinity) to represent all real numbers greater than \(-\frac{25}{7}\).

Answer:

To graph the solution set \(x>-\frac{25}{7}\) (or \(x > - 3.57\) approximately) on the number line:

• Place an open circle at \(-\frac{25}{7}\) (or \(-3.57\)) (since the inequality is \(>\), not \(\geq\)).
• Draw an arrow starting from the open circle and extending to the right (toward positive infinity) to show all values of \(x\) greater than \(-\frac{25}{7}\).

Visually, on the provided number line (with marks at \(-4, - 3, - 2, - 1, 0, 1, 2, 3, 4\)), the open circle is between \(-4\) and \(-3\) (closer to \(-4\), since \(-\frac{25}{7}\approx - 3.57\)), and the arrow points right.