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.

Answer 1

are you sure this is correct

Answer 2

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.

Answer 3

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

1. Starting with the inequality:
\[
-3x \geq 12
\]

2. 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 \(\leq\):
\[
x \leq \frac{12}{-3}
\]

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!