Number Line Notation 679329

1. **State the problem:** We are given a number line with a closed circle at $-7$ and shading extending left to $-\infty$, and a closed circle at $1$ with shading extending right to $\infty$. We need to identify which notation correctly represents this number line. 2. **Analyze the graph:** The shading to the left of $-7$ with a closed circle means $x \leq -7$. The shading to the right of $1$ with a closed circle means $x \geq 1$. 3. **Check each notation:** - $[-7, 1]$ means $-7 \leq x \leq 1$, which is the interval between $-7$ and $1$. This does not match the graph because the graph shows shading outside this interval. - ${x|x \geq -7 \text{ or } x \leq 1}$ means all $x$ such that $x \geq -7$ or $x \leq 1$. This includes all real numbers because any number is either $\geq -7$ or $\leq 1$. This does not match the graph. - ${x| -7 \leq x \leq 1}$ means $x$ between $-7$ and $1$, same as $[-7,1]$, so no. - $(-\infty, -7] \cup [1, \infty)$ means all $x$ less than or equal to $-7$ or greater than or equal to $1$. This matches the graph exactly. 4. **Conclusion:** The correct notation is $$(-\infty, -7] \cup [1, \infty)$$.