QQuestionMathematics
QuestionMathematics
Do I need to flip my sign in the inequality −3x≥12?
A. No
B. Yes
11 months agoReport content
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.
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