Answer :
To determine which expression correctly represents the phrase "Lamar decreased his collection of cards by seven," let's analyze the phrase step-by-step:
1. Identify the variable:
- The phrase mentions "Lamar's collection of cards," which suggests that the number of cards Lamar has can be represented by a variable. Let's use \( x \) to denote the total number of cards Lamar initially has.
2. Understand the operation:
- The phrase states "decreased by seven." This means that the total number of cards Lamar has is reduced by seven.
3. Form the expression:
- If Lamar's initial number of cards is \( x \) and he decreases this number by seven, the correct mathematical expression would be \( x - 7 \).
Now, let's examine the options provided:
1. \( x - 7 \): This directly represents Lamar's original collection \( x \), reduced by seven. This matches the phrase perfectly.
2. \( 7 - x \): This would suggest that seven is being reduced by Lamar's collection, which does not align with the phrase.
3. \( x + 7 \): This expression suggests an increase in the number of cards by seven, which contradicts the idea of a decrease.
4. \( 7x \): This implies multiplying Lamar's collection by seven, which is not relevant to the decrease described in the phrase.
Therefore, the correct expression that represents the phrase "Lamar decreased his collection of cards by seven" is:
[tex]\[ x - 7 \][/tex]
So, the correct answer is option 1.
1. Identify the variable:
- The phrase mentions "Lamar's collection of cards," which suggests that the number of cards Lamar has can be represented by a variable. Let's use \( x \) to denote the total number of cards Lamar initially has.
2. Understand the operation:
- The phrase states "decreased by seven." This means that the total number of cards Lamar has is reduced by seven.
3. Form the expression:
- If Lamar's initial number of cards is \( x \) and he decreases this number by seven, the correct mathematical expression would be \( x - 7 \).
Now, let's examine the options provided:
1. \( x - 7 \): This directly represents Lamar's original collection \( x \), reduced by seven. This matches the phrase perfectly.
2. \( 7 - x \): This would suggest that seven is being reduced by Lamar's collection, which does not align with the phrase.
3. \( x + 7 \): This expression suggests an increase in the number of cards by seven, which contradicts the idea of a decrease.
4. \( 7x \): This implies multiplying Lamar's collection by seven, which is not relevant to the decrease described in the phrase.
Therefore, the correct expression that represents the phrase "Lamar decreased his collection of cards by seven" is:
[tex]\[ x - 7 \][/tex]
So, the correct answer is option 1.
