Can we prove that x>1 implies y<1 if 3x+2y≤5 for real numbers x and y?

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The discussion centers on the mathematical proof that if \( x > 1 \) and \( 3x + 2y \leq 5 \), then it follows that \( y < 1 \). The participants explore the implications of assuming both \( x > 1 \) and \( y \geq 1 \) simultaneously, leading to a contradiction with the given inequality. The conclusion is that the assumption cannot hold true, thereby validating the original statement.

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  • Understanding of real numbers and inequalities
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  • Study algebraic proofs involving inequalities
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Suppose x and y are real numbers and 3x+2y≤5. Prove that if x>1 then y<1
 
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What would happen if x &gt; 1 and y \ge 1 were both true?
 
Not real sure what would happen.
 
This is not an acceptable way to ask for help at homework problems. In addition, it is in the wrong forum.
 

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