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QuestionMathematics

Do I need to flip my sign in the inequality −3x≥12? A. No B. Yes
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Answer

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Step 1:
I'll solve this step-by-step, following the LaTeX formatting guidelines precisely:

Step 2:
: Understand the Inequality

The original inequality is $$-3x \geq 12

Step 3:
: Solve for x by Dividing Both Sides by - 3

\frac{-3x}{-3} \leq \frac{12}{-3}
When dividing an inequality by a negative number, the inequality sign must be flipped.

Step 4:
: Simplify

x \leq -4

Step 5:
: Determine Sign Flip

Since we divided by a negative number (-3), we MUST flip the inequality sign from $$\geq$$ to $$\leq$$.

Step 6:
: Verify

- Original inequality: $$-3x \geq 12
- After solving: x \leq - 4 - The sign was indeed flipped

Final Answer

Yes, you need to flip the sign in the inequality when dividing by a negative number. Key Insight: When multiplying or dividing an inequality by a negative number, the direction of the inequality sign must be reversed to maintain the mathematical truth of the statement.