Question

If 3y + x \(>\) 2 and x + 2y \(\underline<\) 3, What can be said about the value of y?

• A. y= -1
• B. y \(>\) -1
• C. y \(<\) -1
• D. y= 1

Answer 1

The Correct Option is B

Step 1: Solve for \( x \) from the second inequality 

Given the inequality:

\[ x + 2y \leq 3 \]

Solving for \( x \):

\[ x \leq 3 - 2y \]

Step 2: Substitute this into the first inequality

Given the first inequality:

\[ 3y + x > 2 \]

Substituting \( x \leq 3 - 2y \) into the inequality:

\[ 3y + (3 - 2y) > 2 \]

Step 3: Simplify the inequality

\[ 3y + 3 - 2y > 2 \]

\[ y + 3 > 2 \]

\[ y > -1 \]

Conclusion:

Thus, the solution for \( y \) is \( y > -1 \).