Question

Kirk solves the inequality 5 < 12y - 7. Which statement explains the steps he uses to find the solution set of the inequality?
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.
B. Kirk adds 7 to both sides of the inequality and then divides both sides of the equivalent inequality by 12 to get 1 < y.
C. Kirk adds -7 to both sides of the inequality and then divides both sides of the equivalent inequality by 12 to get (- 1/6) < y.
D. Kirk adds 7 to both sides of the inequality, then divides both sides of the equivalent inequality by 12 and reverses the inequality by 12 and reverses the inequality symbol to get 1 > y.

Answer 1

are you sure this is correct

Answer 2

To solve the inequality \(5 < 12y - 7\), Kirk would follow these steps:

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

2. Divide both sides by 12:
\[
\frac{12}{12} < y \implies 1 < y.
\]
This can also be written as \(y > 1\).

Now let's review the options to see which one correctly describes these steps:

A. Kirk adds 7 to both sides of the inequality and then multiplies both sides of the equivalent inequality by 12 to get \(144 < y\).
- This is incorrect because Kirk does not multiply by 12.

B. 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 is correct.

C. Kirk adds -7 to both sides of the inequality and then divides both sides of the equivalent inequality by 12 to get \((-1/6) < y\).
- This is incorrect as he does not add -7.

D. Kirk adds 7 to both sides of the inequality, then divides both sides of the equivalent inequality by 12 and reverses the inequality by 12 and reverses the inequality symbol to get \(1 > y\).
- This is incorrect as there is no need to reverse the inequality.

Thus, the correct statement is **B**.

Answer 3

Yes, let's carefully walk through the solution again for clarity.

The original inequality given is:

\[ 5 < 12y - 7 \]

Let's solve it step-by-step:

1. **Add 7 to both sides** to isolate the term involving \(y\):
\[
5 + 7 < 12y
\]
This simplifies to:
\[
12 < 12y
\]

2. **Divide both sides by 12** to solve for \(y\):
\[
\frac{12}{12} < y
\]
Which simplifies to:
\[
1 < y
\]
This can also be expressed as:
\[
y > 1
\]

Now let's analyze the answer choices again based on these steps:

A. Kirk adds 7 to both sides of the inequality and then multiplies both sides of the equivalent inequality by 12 to get \(144 < y\).
- This is incorrect because there is no multiplication involved at the final step.

B. 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 is correct, as we've shown above.

C. Kirk adds -7 to both sides of the inequality and then divides both sides of the equivalent inequality by 12 to get \((-1/6) < y\).
- This is incorrect; Kirk did not add -7.

D. Kirk adds 7 to both sides of the inequality, then divides both sides of the equivalent inequality by 12 and reverses the inequality by 12 and reverses the inequality symbol to get \(1 > y\).
- This is incorrect because the inequality does not reverse.

The correct choice that accurately explains the steps Kirk used to solve the inequality is indeed **B**: "Kirk adds 7 to both sides of the inequality and then divides both sides of the equivalent inequality by 12 to get \(1 < y\)."

Thank you for prompting a double-check, and I can confirm that this explanation and choice are correct.