Let's break down the problem step by step to find the correct inequality.
1. Understanding the Problem:
- Li's suitcase currently weighs 47.75 pounds.
- The airline charges an extra fee if the suitcase weighs more than 50 pounds.
- We need to find an inequality that determines how much more weight (let's call it [tex]\( x \)[/tex]) can be added without exceeding the 50-pound limit.
2. Setting Up the Inequality:
- Let [tex]\( x \)[/tex] represent the additional weight that can be added to the suitcase.
- The weight of the suitcase after adding [tex]\( x \)[/tex] pounds will be [tex]\( 47.75 + x \)[/tex].
3. Forming the Inequality:
- The suitcase should weigh less than 50 pounds to avoid the extra fee.
- This condition can be written as:
[tex]\[
47.75 + x < 50
\][/tex]
4. Checking the Options:
- Option 1: [tex]\( 47.75 + x < 50 \)[/tex]
- This is the inequality we derived.
- Option 2: [tex]\( 47.75 + x \leq 50 \)[/tex]
- This would mean the weight is allowed to be exactly 50 pounds or less, but the problem specifies to avoid exceeding 50 pounds.
- Option 3: [tex]\( 47.75 + x \geq 50 \)[/tex]
- This implies the weight should be at least 50 pounds, which is incorrect as it would incur an extra fee.
- Option 4: [tex]\( 47.75 + x > 50 \)[/tex]
- This implies the weight should exceed 50 pounds, which also incurs an extra fee.
Hence, the correct inequality that determines how much more weight can be added without going over the 50-pound weight limit is:
[tex]\[
47.75 + x < 50
\][/tex]
