Question

which graph represents the solution set of the following inequality?
-3x - 5 ≥ 7
four number lines with red segments and dots/circles at -4, options as described in the image

Explanation:

Step1: Solve the inequality

Start with \(-3x - 5 \geq 7\). Add 5 to both sides: \(-3x - 5 + 5 \geq 7 + 5\), which simplifies to \(-3x \geq 12\). Then divide both sides by -3 (remember to reverse the inequality sign when dividing by a negative number): \(x \leq -4\).

Step2: Analyze the number line graphs

• A closed circle at -4 (since the inequality is \(\geq\) or \(\leq\), we use a closed circle) and the arrow pointing to the left (because \(x\) is less than or equal to -4, so values to the left of -4 on the number line are included).
• The first graph has a closed circle at -4 and an arrow to the left, which matches our solution \(x \leq -4\). The second graph has an arrow to the right, the third has an open circle (wrong, since the inequality is non - strict), and the fourth has an open circle and arrow to the right.

Answer:

The first graph (with the closed circle at -4 and arrow pointing to the left)