Question

. Which graph represents the solutions to this inequality: 5n−3<3(n+1)
(2 points)
Responses








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Answer 1

To solve the inequality \( 5n - 3 < 3(n + 1) \), let's start by simplifying it step by step.

1. Distribute on the right side:

\[
3(n + 1) = 3n + 3
\]

Now the inequality looks like this:

\[
5n - 3 < 3n + 3
\]

2. Next, we want to isolate \( n \). Subtract \( 3n \) from both sides:

\[
5n - 3n - 3 < 3
\]

This simplifies to:

\[
2n - 3 < 3
\]

3. Now, add \( 3 \) to both sides:

\[
2n < 6
\]

4. 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.