Let's analyze the problem step-by-step:
1. Determine the Total Cost:
- Each box of cereal costs [tex]$3.
- Alexis buys \( x \) boxes of cereal.
- Therefore, the total cost for \( x \) boxes of cereal is given by the expression \( 3x \).
2. Calculate the Change:
- Alexis pays with a $[/tex]20 bill.
- To find out the change she should receive, we need to subtract the total cost of the cereal [tex]\( 3x \)[/tex] from the [tex]$20 she paid.
- The expression for the change can be written as \( 20 - 3x \).
Now, let's examine the provided options one by one to see which one matches our derived expression:
1. Option 1: \( 20 - 3x \)
- This is exactly the expression we derived. It represents the amount of change Alexis should receive after buying \( x \) boxes of cereal at $[/tex]3 each and paying with a $20 bill.
2. Option 2: [tex]\( (3 - 20)x \)[/tex]
- Simplifying this expression gives [tex]\( -17x \)[/tex], which does not represent the change correctly. It suggests a relationship where [tex]\( 3 \)[/tex] is subtracted from [tex]\( 20 \)[/tex] before being multiplied by [tex]\( x \)[/tex], which doesn't align with our understanding of the problem.
3. Option 3: [tex]\( 3x - 20 \)[/tex]
- This expresses the total cost minus 20, which indicates a negative value in normal purchasing scenarios where the total cost is less than or equal to the amount paid. This does not represent the change Alexis should receive correctly.
4. Option 4: [tex]\( (20 - 3)x \)[/tex]
- Simplifying this expression gives [tex]\( 17x \)[/tex], meaning [tex]\( x \)[/tex] is multiplied by [tex]\( (20 - 3) \)[/tex], which again does not match the scenario of paying and receiving change.
Therefore, the correct expression that represents the total amount of change Alexis should receive is:
[tex]\[ \boxed{20 - 3x} \][/tex]
