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Kirk solves the inequality 5<12y−7. Which statement explains the steps he uses to find the solution set of the inequality?(1 po...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, 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 (−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 divides both sides of the equivalent inequality by 12 to get 1<y.
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GPT-4o mini
Let's solve the inequality step-by-step:
The original inequality is:
\[ 5 < 12y - 7 \]
1. **Add 7 to both sides:**
\[ 5 + 7 < 12y \]
\[ 12 < 12y \]
2. **Divide both sides by 12:**
\[ \frac{12}{12} < y \]
\[ 1 < y \]
This can also be written as:
\[ y > 1 \]
Now, looking at the statements:
- Kirk adds 7 to both sides of the inequality and then divides both sides of the equivalent inequality by 12 to get 1 < y.
The statement "Kirk adds 7 to both sides of the inequality and then divides both sides of the equivalent inequality by 12 to get 1 < y" accurately reflects the steps taken to solve the inequality without any mistakes regarding reversing the inequality symbol or any incorrect operations.
Thus, the correct response 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.**
The original inequality is:
\[ 5 < 12y - 7 \]
1. **Add 7 to both sides:**
\[ 5 + 7 < 12y \]
\[ 12 < 12y \]
2. **Divide both sides by 12:**
\[ \frac{12}{12} < y \]
\[ 1 < y \]
This can also be written as:
\[ y > 1 \]
Now, looking at the statements:
- Kirk adds 7 to both sides of the inequality and then divides both sides of the equivalent inequality by 12 to get 1 < y.
The statement "Kirk adds 7 to both sides of the inequality and then divides both sides of the equivalent inequality by 12 to get 1 < y" accurately reflects the steps taken to solve the inequality without any mistakes regarding reversing the inequality symbol or any incorrect operations.
Thus, the correct response 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.**
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