Let's solve the inequality step-by-step to determine the correct response.
Starting with the inequality: \[ 5 < 12y - 7 \]
Step 1: Add 7 to both sides: \[ 5 + 7 < 12y \] \[ 12 < 12y \]
Step 2: Divide both sides by 12: \[ \frac{12}{12} < y \] \[ 1 < y \] This can also be expressed as: \[ y > 1 \]
Now, we'll compare this result with the responses:
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Option A states that he adds 7 and then multiplies by 12, which is incorrect since we divided by 12, not multiplied.
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Option B states he adds -7 (incorrect), and then divides by 12. This doesn't correctly depict what happened in our steps.
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Option C mentions adding 7 and dividing by 12 and reversing the inequality symbol, which is incorrect because there's no need to reverse the symbol here.
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Option D correctly states that he adds 7 and then divides by 12 to get \( 1 < y \).
The correct response is D: Kirk adds 7 to both sides of the inequality and then divides both sides of the equivalent inequality by 12 to get 1 < y.