Question

choose the graph of the solution to the inequality $x < -12$.

Explanation:

Step1: Analyze inequality symbol

The inequality is $x < -12$, which means $x$ is strictly less than -12. For strict inequalities ($<$ or $>$), we use an open circle on the number line to show the value itself is not included.

Step2: Determine direction of shading

Since $x$ is less than -12, we shade all values to the left of -12 on the number line (left represents smaller numbers).

Step3: Match to options

• The first two options shade to the right, which is for values greater than a number, so they are incorrect.
• The fourth option uses a closed circle, which is for non-strict inequalities ($\leq$ or $\geq$), so it is incorrect.
• The third option has an open circle and shading to the left, which matches $x < -12$.

Answer:

The correct graph is the third option: <point>81 582</point> (the number line with an open circle at -10, shading leftward to negative infinity)