Question

graph the inequality below on the number line.\\(x < 6\\)

Explanation:

Step1: Identify the critical point

The inequality is \( x < 6 \), so the critical number is 6.

Step2: Determine the type of dot

Since the inequality is \( < \) (not \( \leq \)), we use an open circle at 6 to show that 6 is not included in the solution set.

Step3: Determine the direction of the line

For \( x < 6 \), the solutions are all numbers less than 6, so we draw an arrow to the left of 6 on the number line, covering all numbers from negative infinity up to (but not including) 6.

To graph it:

1. Locate 6 on the number line.
2. Draw an open circle at 6 (because \( x \) is strictly less than 6, not equal to 6).
3. Draw a line with an arrow starting from the open circle and going to the left (towards smaller numbers) to represent all values of \( x \) that are less than 6.

Answer:

To graph \( x < 6 \) on the number line:

• Place an open circle at 6 (since \( x \) does not equal 6).
• Draw a line with an arrow pointing to the left of 6 (toward negative infinity) to show all numbers less than 6 are included in the solution.