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

Answer 1

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

1. Distribute 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 \( n < 3 \).

Now, to choose the correct graph representing this inequality, you would look for a graph that shows a number line with an open circle at \( n = 3 \) and a shaded region to the left, indicating that all values less than 3 are included in the solution.

If you have specific graph options, please share them, and I can help identify the correct one.