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Which graph represents the solutions to this inequality: 5n−3<3(n+1) (1 point) ResponsesQuestion
15. Which graph represents the solutions to this inequality: 5n−3<3(n+1) (2 points) Responses
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GPT-4o mini
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.
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.
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