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

A.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 .

B.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 .

C.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 .

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

Answer 1

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:

- **Option A** states that he adds 7 and then multiplies by 12, which is incorrect since we divided by 12, not multiplied.

- **Option B** states he adds -7 (incorrect), and then divides by 12. This doesn't correctly depict what happened in our steps.

- **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.

- **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**.