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The image presents the question: "Which inequality is equivalent to \( -x < 12 \)?"

Let's solve this inequality:

Given:
\[
- x < 12
\]

1. To solve for \( x \), we need to eliminate the negative sign. To do that, multiply both sides of the inequality by \(-1\). However, keep in mind that multiplying or dividing by a negative number reverses the inequality sign. So:
\[
x > -12
\]

Thus, the inequality equivalent to \( -x < 12 \) is:
\[
x > -12
\]

In the options provided in the image, the correct answer is the third option: \( x > -12 \).

Would you like further explanation or have any questions? Here are some related questions:

1. What is the rule for reversing an inequality when multiplying or dividing by a negative number?
2. How do you solve inequalities that involve absolute values?
3. Can inequalities have multiple solutions? If so, how do we represent them?
4. What happens to an inequality when you add or subtract the same value from both sides?
5. How can inequalities be represented graphically on a number line?

**Tip**: Always remember to flip the inequality sign when multiplying or dividing both sides by a negative number!

Which inequality is equivalent to -x < 12?

Learn how to solve the inequality -x < 12. This problem covers key algebra concepts, including the rule for reversing inequalities when multiplying or dividing by a negative number. Suitable for students in Grades 6-8.

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