Question

|3n - 21 - 2 < 1. How to graph it?

A) n > 8
B) n < 8
C) n > 11
D) n < 11

Answer 1

To graph the inequality |3n - 21| - 2 < 1, we solve for two separate cases for the absolute value expression to find n < 8 and n > 6. The solution is the intersection of these two inequalities, resulting in the correct answer of n < 8 (option B). This is represented on a number line with open circles at 6 and 8 and shading in between.

Step-by-step explanation:

To graph the inequality |3n - 21| - 2 < 1, we first need to isolate the absolute value expression. Adding 2 to both sides, we get |3n - 21| < 3. An absolute value inequality like this one means the expression inside the absolute value is less than 3 units away from 0 on the number line. This gives us two inequalities to solve:

• 3n - 21 < 3
• 3n - 21 > -3

Now we solve each inequality separately.

For 3n - 21 < 3:

1. Add 21 to both sides: 3n < 24
2. Divide by 3: n < 8

For 3n - 21 > -3:

1. Add 21 to both sides: 3n > 18
2. Divide by 3: n > 6

Our solution is the intersection of n < 8 and n > 6, which we graph on a number line. We use an open circle at 8 because n is less than 8, not equal to it, and we shade all numbers between 8 and 6. We also use an open circle at 6 for the same reason. The correct graph represents all the numbers between 6 and 8, not including 6 and 8 themselves.

Therefore, the correct answer is n < 8, which corresponds to option B).