Russel wants to buy 3 identical gift cards. He wants to make sure his total cost is no more than $2 above or below $60. Which of the following inequalities represents this situation?

Let's define the variables and set up the inequality:

- Let the cost of one gift card be $ x $.
- Russel is buying 3 identical gift cards, so the total cost is $ 3x $.
- He wants the total cost to be within $2 of $60. This means the total cost can be no more than $2 above or below $60.

This translates to the following inequality:

\[
|3x - 60| \leq 2
\]

This absolute value inequality represents the total cost being within $2 of $60. To break this down into two inequalities without the absolute value:

\[
-2 \leq 3x - 60 \leq 2
\]

Now, add 60 to all sides of the inequality:

\[
58 \leq 3x \leq 62
\]

Thus, the inequality representing this situation is:

\[
58 \leq 3x \leq 62
\]

Would you like more details or have any questions?

Here are 5 related questions to explore:

1. How do you solve absolute value inequalities in general?
2. What if Russel wanted to buy 4 gift cards instead?
3. How would the inequality change if the range was $5 instead of $2?
4. What happens if Russel wants the total cost to be exactly $60?
5. How would the inequality change if the price of each gift card varies by tax?

**Tip:** When dealing with absolute value inequalities, remember that they split into two separate inequalities, one positive and one negative.

Learn how to solve an absolute value inequality involving Russel's purchase of 3 identical gift cards, where the total cost must be within $2 of $60. This problem covers algebraic concepts related to inequalities and absolute values, suitable for students in Grades 6-8.

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