Questions: Graph the set x x ≤ 5 on the number line. Then, write the set using interval notation. x x ≤ 5=

Transcript text: Graph the set $\{x \mid x \leq 5\}$ on the number line. Then, write the set using interval notation. \[ \{x \mid x \leq 5\}= \] $\square$

Solution

Solution Steps

Step 1: Understand the Set

The given set is $\{x \mid x \leq 5\}$. This means we are looking for all values of $x$ that are less than or equal to 5.

Step 2: Graph the Set on the Number Line

To graph $\{x \mid x \leq 5\}$ on the number line:

Draw a number line.
Shade the region to the left of 5, including 5 itself (since $x$ can be equal to 5).

Step 3: Write the Set Using Interval Notation

The interval notation for the set $\{x \mid x \leq 5\}$ is $(-\infty, 5]$. This notation indicates that $x$ can be any value from negative infinity up to and including 5.