Choose the correct description of the graph of the compound inequality: ( 5 points) \( x-3<-9 \) or \( x+5 \geq 12 \) A number line with a closed circle on -6 , shading to the left, and an open circle on 7 , shading to the right A number line with an open circle on -6 , a closed circle on 7 , and shading in between A number line with an open circle on -6 , shading to the left, and a closed circle on 7 , shading to the right A number line with a closed circle on -6 , an open circle on 7 , and shading in between

To solve the compound inequality \( x-3 < -9 \) or \( x+5 \geq 12 \), we first break down each part. For \( x-3 < -9 \), adding 3 gives \( x < -6 \). So, we have an open circle on -6 with shading to the left. For \( x+5 \geq 12 \), subtracting 5 gives \( x \geq 7 \). This results in a closed circle on 7 with shading to the right. Thus, the correct description is the one with an open circle on -6, shading to the left, and a closed circle on 7, shading to the right. So, the answer is: A number line with an open circle on -6 , shading to the left, and a closed circle on 7 , shading to the right. To visualize these inequalities, think of them as two distinct groups: one of all numbers less than -6 and another beginning at 7 and extending towards infinity! It’s like having two parties, and only those with the right invitation can join!