Mathematics 15. Which values make the inequality \( 2 y+3>3 y \) true? Select all the correct answers. A. \( y=0 \) B. \( y=1 \) C. \( y=2 \) D. \( y=3 \) E. \( y=4 \)

To solve the inequality \( 2y + 3 > 3y \), we first rearrange the equation by subtracting \( 2y \) from both sides, giving us \( 3 > 3y - 2y \) or, simplified, \( 3 > y \). This means any value of \( y \) that is less than 3 will satisfy the inequality. Now, plugging in the options: - \( y = 0 \): True (0 < 3) - \( y = 1 \): True (1 < 3) - \( y = 2 \): True (2 < 3) - \( y = 3 \): False (3 is not less than 3) - \( y = 4 \): False (4 is not less than 3) So, the correct answers are **A, B, and C**. Plugging these values into the inequality not only helps you understand the solution but can also highlight some simple techniques in manipulating inequalities as well. Watch out for that sneaky "greater than" vs. "less than" switch!