QQuestionMathematics
QuestionMathematics
Solve the inequality:
3x ≥ 12
Rearrange it so that x comes first.
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Answer
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Step 1:I'll solve this step-by-step using the precise LaTeX formatting guidelines:
Step 2:: Identify the original inequality
The original inequality is $$3x \geq 12
Step 3:: Isolate x by dividing both sides by 3
\frac{3x}{3} \geq \frac{12}{3}
To solve for x, divide both sides of the inequality by 3:
Step 4:: Simplify the inequality
x \geq 4
Step 5:: Check the solution
- We divided by a positive number (3), so the inequality direction remains the same - The solution means all real numbers greater than or equal to 4 satisfy the original inequality
Final Answer
Key Insights: - When solving inequalities, divide or multiply both sides by the same number - If dividing by a positive number, the inequality sign remains unchanged - The solution represents all numbers on the number line from 4 to positive infinity
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