Question

graph the inequality below on the number line.
$b < 4$
number line from -11 to 11 with ticks at each integer

Explanation:

Step1: Identify the critical point

The inequality is \( b < 4 \), so the critical value is 4. Since the inequality is strict (\(<\), not \(\leq\)), we use an open circle at 4 to indicate that 4 is not included in the solution set.

Step2: Determine the direction of the line

For \( b < 4 \), we shade all the numbers to the left of 4 on the number line because those are the values of \( b \) that are less than 4.

To graph it:

1. Locate 4 on the number line.
2. Draw an open circle at 4 (because \( b \) cannot be equal to 4).
3. Draw a line with an arrow pointing to the left from the open circle to represent all numbers less than 4.

Answer:

To graph \( b < 4 \) on the number line:

• Place an open circle at \( 4 \) (since \( 4 \) is not included in the solution).
• Draw a ray (line with an arrow) starting from the open circle and extending to the left (toward negative infinity) to represent all values of \( b \) that are less than \( 4 \).

(Visually, on the given number line, the open circle is at the tick mark labeled \( 4 \), and the arrow points left past \( 3, 2, 1, 0, -1, \dots \))