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

Question

(2 points)
Responses

Answer 1

To solve the inequality \( 5n - 3 < 3(n + 1) \), follow these steps:

1. Distribute the \(3\) on the right side: \[ 5n - 3 < 3n + 3 \]

2. Subtract \(3n\) from both sides: \[ 5n - 3n - 3 < 3 \] \[ 2n - 3 < 3 \]

3. Add \(3\) to both sides: \[ 2n < 6 \]

4. Divide both sides by \(2\): \[ n < 3 \]

The solution to the inequality is \( n < 3 \).

Graphical Representation

This solution can be represented on a number line:

• There will be an open circle at \(3\) (indicating that \(3\) is not included in the solution).
• The line will extend to the left towards negative infinity, indicating that all numbers less than \(3\) are included in the solution.

In a graph representing this inequality:

• The x-axis will have a point marked at \(3\) with an open circle.
• The shaded area will extend to the left from \(3\), indicating all the values less than \(3\).

If you have graph options, you're looking for one that matches this description.