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{:("Column A",2x + 1 > 3x + 2 and 5x + 2...

`{:("Column A",2x + 1 > 3x + 2 and 5x + 2 > 4x, "Column B"),(x,,1):}`

A

If column A is larger

B

If column B is larger

C

If the columns are equal

D

If there is not enough information to decide

Text Solution

AI Generated Solution

The correct Answer is:
To solve the given problem, we need to analyze the inequalities provided in Column A and compare the result with the value in Column B. ### Step-by-Step Solution: 1. **Write down the inequalities:** The inequalities given in Column A are: - \( 2x + 1 > 3x + 2 \) - \( 5x + 2 > 4x \) 2. **Solve the first inequality:** - Start with \( 2x + 1 > 3x + 2 \). - Rearranging gives: \[ 2x + 1 - 3x - 2 > 0 \implies -x - 1 > 0 \implies -x > 1 \implies x < -1 \] 3. **Solve the second inequality:** - Start with \( 5x + 2 > 4x \). - Rearranging gives: \[ 5x + 2 - 4x > 0 \implies x + 2 > 0 \implies x > -2 \] 4. **Combine the results:** - From the first inequality, we have \( x < -1 \). - From the second inequality, we have \( x > -2 \). - Therefore, the combined result is: \[ -2 < x < -1 \] 5. **Compare with Column B:** - Column A has \( x \) which lies between -2 and -1. - Column B has the constant value \( 1 \). - Since any value of \( x \) in the range \( -2 < x < -1 \) is less than \( 1 \), we conclude that: \[ x < 1 \] ### Conclusion: - Since \( x \) is always less than \( 1 \), we can say that Column A is less than Column B. ### Final Answer: - Column A < Column B.
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