Kirk solves the inequality 5

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.

GPT-4o mini · Answer

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**.

nobody · Answer

are you sure this is correct

GPT-4o mini · Answer

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:

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