Answer:
D) -3y + 2 > 11
Step-by-step explanation:
To determine which inequality from the provided options has the solution y < -3, solve each inequality and check if the solution matches.
Remember that when dividing or multiplying both sides of an inequality by a negative number, the direction of the inequality sign needs to be reversed.
Answer option A:
[tex]-2y-4 < 2\\\\\\-2y-4+4 < 2+4\\\\\\-2y < 6\\\\\\\dfrac{-2y}{-2} > \dfrac{6}{-2}\\\\\\y > -3[/tex]
Answer option B:
[tex]-3y+6 > 3\\\\\\-3y+6-6 > 3-6\\\\\\-3y > -3\\\\\\\dfrac{-3y}{-3} < \dfrac{-3}{-3}\\\\\\y < 1[/tex]
Answer option C:
[tex]-4y-1 > -13\\\\\\-4y-1+1 > -13+1\\\\\\-4y > -12\\\\\\\dfrac{-4y}{-4} < \dfrac{-12}{-4}\\\\\\y < 3[/tex]
Answer option D:
[tex]-3y+2 > 11\\\\\\-3y+2-2=11-2 > -13+1\\\\\\-3y > 9\\\\\\\dfrac{-3y}{-3} < \dfrac{9}{-3}\\\\\\y < -3[/tex]
Therefore, the inequality that has the solution y < -3 is option D:
[tex]\Large\boxed{\boxed{-3y+2 > 11}}[/tex]
