Kirk solves the inequality 5<12y−7. Which statement explains the steps he uses to find the solution set of the inequality?(1 point)

Question

Responses

Kirk adds 7 to both sides of the inequality and then divides both sides of the equivalent inequality by 12 to get 1<y.
Kirk adds 7 to both sides of the inequality and then divides both sides of the equivalent inequality by 12 to get 1 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 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 and then multiplies both sides of the equivalent inequality by 12 to get 144<y.

Answer 1

To solve the inequality \( 5 < 12y - 7 \), Kirk would proceed with the following steps:

1. Add 7 to both sides of the inequality: \[ 5 + 7 < 12y - 7 + 7 \] which simplifies to: \[ 12 < 12y. \]

2. Divide both sides of the resulting inequality by 12: \[ \frac{12}{12} < \frac{12y}{12} \] which simplifies to: \[ 1 < y. \]

This means the solution set for the inequality is \( y > 1 \).

Given the response options, the correct statement that explains Kirk's steps is:

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