Let's solve the problem step by step:
1. Understand the problem: You have a maximum weight limit of 50 pounds before an overweight fee is applied, and your empty shipping box weighs 2 pounds. You need to find out how many pounds, [tex]\( x \)[/tex], you can pack in the box without exceeding the weight limit.
2. Set up the inequality: The total weight of the box including the contents should be less than or equal to 50 pounds.
- Weight of the contents: [tex]\( x \)[/tex] pounds
- Weight of the empty box: 2 pounds
- Combined weight: [tex]\( x + 2 \)[/tex] pounds
We can express this situation with the inequality:
[tex]\[
x + 2 \leq 50
\][/tex]
3. Solve the inequality:
[tex]\[
x + 2 \leq 50
\][/tex]
Subtract 2 from both sides to isolate [tex]\( x \)[/tex]:
[tex]\[
x \leq 50 - 2
\][/tex]
Simplify the right side:
[tex]\[
x \leq 48
\][/tex]
So, the correct inequality that shows how many pounds you can pack in the shipping box without paying an overweight fee is:
[tex]\[
x + 2 \leq 50
\][/tex]
and solving it gives:
[tex]\[
x \leq 48
\][/tex]
Therefore, the correct option is:
A. [tex]\( x+2 \leq 50 \)[/tex], [tex]\( x \leq 48 \)[/tex].
