To determine how much more money Li's family needs to save to reach their goal of at least [tex]$5,000, we can set up an inequality.
1. Current Situation:
Li's family's vacation savings account currently has a balance of $[/tex]2,764.
2. Savings Goal:
They aim to have at least [tex]$5,000 in their vacation savings account.
3. Unknown Amount Needed:
Let \( x \) represent the additional amount of money the family still needs to save in order to reach $[/tex]5,000.
The situation can be described with the following relationship:
[tex]\[ 2764 + x \][/tex]
4. Formulating the Inequality:
To find the amount they need, this total should be at least [tex]$5,000. "At least" means the same as "greater than or equal to." Therefore, we can write the inequality as:
\[ 2764 + x \geq 5000 \]
5. Checking Other Options:
- \( 2764 + x > 5000 \) implies the total must be strictly greater than $[/tex]5,000. This means [tex]$5,000 exactly wouldn't be enough, which doesn't match the requirement of at least $[/tex]5,000.
- [tex]\( 2764 + x \leq 5000 \)[/tex] implies the total can be [tex]$5,000 or less, which conflicts with them needing at least $[/tex]5,000.
- [tex]\( 5000 + x > 2764 \)[/tex] rearranges the roles and does not correctly represent the amount needing to be added to their current savings.
Therefore, the correct inequality that can be used to determine the amount of money Li's family still needs to save is:
[tex]\[ 2764 + x \geq 5000 \][/tex]
This ensures that their total savings will be at least $5,000.
