Question
Choose the true statement about the graph of \( 3 x \geq 6 \). closed circle on 2 and all numbers to the right shaded open circle on 2 and all numbers to the right shaded olosed circle on 2 and all numbers to the left shaded numbers to the left shaded
Ask by Savage Blake. in the United States
Feb 25,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The correct graph has a closed circle at 2 and shading to the right.
Solution
We start with the inequality 3x ≥ 6. Dividing both sides by 3 (which is positive, so the inequality remains the same) gives:
x ≥ 2.
This means that 2 is included in the solution, and all numbers greater than 2 are also included.
The correct graph is represented by a closed circle at 2 (indicating that 2 is included) and shading to the right of 2 (indicating that all numbers greater than or equal to 2 are part of the solution).
Thus, the true statement is:
"closed circle on 2 and all numbers to the right shaded."
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Simplify this solution Extra Insights
To solve the inequality \(3x \geq 6\), we first divide both sides by 3, which gives us \(x \geq 2\). This means we need a closed circle on 2 (since 2 is included in the solution) and shade all numbers to the right, indicating all values greater than 2 satisfy the inequality. It's always a good idea to double-check your boundaries! Remember, if you see a symbol like \(\leq\) or \(\geq\), it indicates the boundary point is included and should have a closed circle. On the flip side, if you encounter a symbol like \(<\) or \(>\), you should use an open circle to show that the boundary is not part of the solution! Keep practicing, and soon these will become second nature!
