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A package can weigh at most 50 pounds before you must pay an overweight fee. Your empty shipping box weighs 2 pounds.

Write and solve an inequality that shows how many pounds, [tex]$x$[/tex], you can pack in the shipping box without paying the fee.

A. [tex]x + 2 \leq 50[/tex]
[tex]x \leq 48[/tex]

B. [tex]x + 2 \leq 50[/tex]
[tex]x \leq 52[/tex]

C. [tex]x - 2 \geq 50[/tex]
[tex]x \geq 52[/tex]

D.
[tex]
\begin{array}{l}
x + 2 \ \textgreater \ 50 \\
x \ \textgreater \ 48
\end{array}
[/tex]


Sagot :

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].
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