Mary Ann solves the inequality -3x _ 12. Justify the steps Mary Ann takes to find the solution set.

Question

Mary Ann solves the inequality -3x >_ 12. Justify the steps Mary Ann takes to find the solution set. A. Mary Ann adds -3 to both sides of the inequality to get x >_ 9. B. Mary Ann divides both sides of the inequality by -3 and changes the inequality symbol to <_ to get x <_ -4. C. Mary Ann divides both sides of the inequality by -3 to get x >_ -4. D. Mary Ann adds -3 to both sides of the inequality and changes the inequality symbol to <_ to get x <_ 9.

GPT-4o mini · Answer

To solve the inequality $-3x \geq 12$, Mary Ann needs to isolate $x$. Here’s the correct justification for the steps she should take: 1. First, to isolate $x$, Mary Ann must divide both sides of the inequality by $-3$. However, when dividing or multiplying both sides of an inequality by a negative number, the direction of the inequality symbol must also be reversed. So, if she divides both sides by $-3$, the steps would look like this: $$ -3x \geq 12 $$ Dividing both sides by $-3$: $$ x \leq \frac{12}{-3} $$ This simplifies to: $$ x \leq -4 $$ Hence, the correct justification from the given options would be: **B. Mary Ann divides both sides of the inequality by -3 and changes the inequality symbol to ≤ to get x ≤ -4.** The other options are incorrect because they either add or do not properly change the inequality sign when dividing by a negative.

nobody · Answer

are you sure this is correct

GPT-4o mini · Answer

Yes, I am sure. Let's carefully go through the steps to solve the inequality $-3x \geq 12$ again.

Starting with the inequality: \[ -3x \geq 12 \]
To isolate $x$, we need to divide both sides by $-3$. However, when dividing or multiplying both sides of an inequality by a negative number, we must reverse the inequality sign. So, when we divide both sides by $-3$, the inequality changes from $\geq$ to $\leq$: \[ x \leq \frac{12}{-3} \]
Simplifying the right side gives us: \[ x \leq -4 \]

So the solution to the inequality is $x \leq -4$.

Thus, the correct step that justifies Mary Ann's solution is:

B. Mary Ann divides both sides of the inequality by -3 and changes the inequality symbol to ≤ to get x ≤ -4.

If you have any further questions or need clarification on any part of this process, feel free to ask!