Which graph represents the compound inequality 3 n 1

General
1

which graph represents the compound inequality 3 n 1

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Which graph represents the compound inequality 3n ≥ 1?

Answer:

To properly address the compound inequality involving 3n, we first need to ensure we interpret it correctly. Let’s consider the inequality expressed as 3n ≥ 1.

Step-by-Step Solution

  1. Isolate the Variable:
    To isolate the variable ( n ), divide both sides of the inequality by 3:

    \frac{3n}{3} \geq \frac{1}{3}

    Simplifying this, we get:

    n \geq \frac{1}{3}

  2. Graphing the Inequality:
    The solution to this inequality will be all values of ( n ) that are greater than or equal to ( \frac{1}{3} ).

    • On a number line, locate ( \frac{1}{3} ).
    • Since the inequality is ( \geq ), we’ll include ( \frac{1}{3} ) itself in our solution, denoted by a closed circle (●) at ( \frac{1}{3} ).
    • Shade the number line to the right of ( \frac{1}{3} ) to indicate all numbers greater than ( \frac{1}{3} ).

  3. Visual Representation:
    Here is what the graph of ( n \geq \frac{1}{3} ) would look like on a number line:

     -----------------|-------->
                 1/3

    The closed circle at ( 1/3 ) indicates that ( 1/3 ) is part of the solution, and the arrow pointing to the right indicates all numbers greater than ( 1/3 ).

Conclusion:

So, the graph representing the inequality ( 3n \geq 1 ) or equivalently ( n \geq \frac{1}{3} ) is a number line with a closed circle at ( \frac{1}{3} ) and shading to the right of ( \frac{1}{3} ).

If you have any additional constraints or if the compound inequality is more complex, please provide further details, and I can offer more specific guidance.