Question

Kirk solves the inequality 5<12y−7 . Which statement explains the steps he uses to find the solution set of the inequality?(1 point) Responses Kirk adds −7 to both sides of the inequality and then divides both sides of the equivalent inequality by 12 to get (−16)<y. Kirk adds negative 7 to both sides of the inequality and then divides both sides of the equivalent inequality by 12 to get left parenthesis negative Start Fraction 1 over 6 End Fraction right parenthesis less than y . Kirk adds 7 to both sides of the inequality, then divides both sides of the equivalent inequality by 12 and reverses the inequality symbol to get 1>y. Kirk adds 7 to both sides of the inequality, then divides both sides of the equivalent inequality by 12 and reverses the inequality symbol to get 1 greater than y . Kirk adds 7 to both sides of the inequality and then multiplies both sides of the equivalent inequality by 12 to get 144<y. Kirk adds 7 to both sides of the inequality and then multiplies both sides of the equivalent inequality by 12 to get 144 less than y . Kirk adds 7 to both sides of the inequality and then divides both sides of the equivalent inequality by 12 to get 1<y.

Answer 1

Let's solve the inequality step by step:

1. Start with the given inequality:
   \( 5 < 12y - 7 \)

2. Add 7 to both sides:
   \( 5 + 7 < 12y \)
   \( 12 < 12y \)

3. Divide both sides by 12:
   \( \frac{12}{12} < y \)
   \( 1 < y \)
   or
   \( y > 1 \)

Kirk’s correct procedure is to add 7 and then divide by 12 to isolate \( y \). The correct statement that explains these steps is:

"Kirk adds 7 to both sides of the inequality and then divides both sides of the equivalent inequality by 12 to get \( 1 < y \)."

This option accurately describes the operations performed to solve the inequality correctly.