Question

1. graph $t < 6$ on the number line.

(number line with marks at 0,1,2,3,4,5,6,7,8,9,10)

Explanation:

Step1: Analyze the inequality

The inequality is \( t < 6 \), which means we need to represent all real numbers less than 6 on the number line.

Step2: Determine the type of dot

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

Step3: Determine the direction of the line

For values less than 6, we draw a line to the left of the open circle at 6, covering all numbers from negative infinity up to (but not including) 6. On the given number line, this means the line should extend from the open circle at 6 towards 0, 1, 2, 3, 4, 5 and beyond to the left.

Answer:

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

1. Place an open circle at 6 (because \( t = 6 \) is not a solution).
2. Draw a line segment (or an arrow) starting from the open circle at 6 and extending to the left (towards smaller numbers) to represent all numbers less than 6.

The correct graph should have an open circle at 6 and a line (or arrow) pointing to the left (covering 0, 1, 2, 3, 4, 5 and beyond to the left of 0).