Question

Which graph shows the solution set for Negative five-halves x minus 3 less-than-or-equal-to 2?
A number line going from negative 8 to positive 2. An open circle is at negative 2. Everything to the left of the circle is shaded.
A number line going from negative 8 to positive 2. An open circle is at negative 2. Everything to the right of the circle is shaded.
A number line going from negative 8 to positive 2. A closed circle is at negative 2. Everything to the left of the circle is shaded.
A number line going from negative 8 to positive 2. A closed circle is at negative 2. Everything to the right of the circle is shaded.

Answer 1

To solve the inequality \(-\frac{5}{2}x - 3 \leq 2\), we first isolate \(x\):

1. Add \(3\) to both sides:
\[
-\frac{5}{2}x \leq 2 + 3
\]
\[
-\frac{5}{2}x \leq 5
\]

2. Now, multiply both sides by \(-\frac{2}{5}\). Remember that when you multiply or divide by a negative number, you must reverse the inequality sign:
\[
x \geq 5 \times -\frac{2}{5}
\]
\[
x \geq -2
\]

This means the solution set for the inequality is \(x\) values greater than or equal to \(-2\).

- This corresponds to a closed circle at \(-2\) (since the inequality is \(\leq\)) and shading to the right (to indicate all values greater than \(-2\)).

Thus, the correct graph showing the solution set would be:
**A number line going from negative 8 to positive 2. A closed circle is at negative 2. Everything to the right of the circle is shaded.**