Question

1. the data plan on your familys cell phone costs more if your family uses more than \\(5\text{ gb}\\) in a month. write an inequality to show how much data your family can use without being charged more.

\\(\bigcirc\\) \\(5 = d\\)

\\(\bigcirc\\) \\(5 < d\\)

\\(\bigcirc\\) \\(5 \le d\\)

\\(\bigcirc\\) \\(5 \ge d\\)

Explanation:

⚡ Using what you learned: understanding inequalities

Step 1: Identify the variable and the limit

Let \( d \) represent the amount of data your family uses in gigabytes (GB).

The problem states that the plan costs more if your family uses more than \( 5\text{ GB} \). This means:

• Charged more if: \( d > 5 \)

Step 2: Determine the condition for not being charged more

To avoid being charged more, your family must use an amount of data that is not more than \( 5\text{ GB} \).

This means the data usage \( d \) must be less than or equal to \( 5\text{ GB} \):

$$ d \le 5 $$

Step 3: Match with the given options

We can rewrite the inequality \( d \le 5 \) by swapping the sides and reversing the inequality sign:

$$ 5 \ge d $$

This matches the fourth option.

Answer:

\( 5 \ge d \)