To solve the inequality \( 5n - 3 < 3(n + 1) \), let's start by simplifying it step by step.
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Distribute on the right side:
\[ 3(n + 1) = 3n + 3 \]
Now the inequality looks like this:
\[ 5n - 3 < 3n + 3 \]
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Next, we want to isolate \( n \). Subtract \( 3n \) from both sides:
\[ 5n - 3n - 3 < 3 \]
This simplifies to:
\[ 2n - 3 < 3 \]
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Now, add \( 3 \) to both sides:
\[ 2n < 6 \]
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Finally, divide both sides by \( 2 \):
\[ n < 3 \]
The solution to the inequality is \( n < 3 \).
Now, when looking at the graph representations, you would look for a number line where the area to the left of \( 3 \) is shaded, and there is an open circle at \( 3 \) to indicate that \( n = 3 \) is not included in the solutions.
If you have specific graph options, you can select the one that corresponds to this description.