Which graph represents the solutions to this inequality: 5n−3<3(n+1)
To solve the inequality, we can simplify both sides first:
5n - 3 < 3(n + 1)
5n - 3 < 3n + 3
Next, we can isolate the terms with n on one side of the inequality:
5n - 3 - 3n < 3
2n - 3 < 3
Then, we can add 3 to both sides:
2n - 3 + 3 < 3 + 3
2n < 6
Finally, we can divide both sides by 2:
2n / 2 < 6 / 2
n < 3
Therefore, the solutions to the inequality are n < 3. The graph representing this inequality would be an open circle at 3 on the number line with an arrow pointing to the left, indicating that any value less than 3 would be a solution.
To determine which graph represents the solutions to the inequality 5n - 3 < 3(n+1), we can start by simplifying the inequality:
5n - 3 < 3n + 3
Next, let's move all the terms involving 'n' to one side of the inequality:
5n - 3n < 3 + 3
2n < 6
Now, we can divide both sides of the inequality by 2 to solve for 'n':
n < 3
So, the solutions to the inequality are all values of 'n' that are less than 3.
Now, let's see which graph represents this inequality. Since the inequality is "less than", the graph would be represented by an open circle on 3 and then shading to the left of 3.
Here is a visual representation of the graph:
-----o-------------->
-3 0 3 6 9 12
The open circle represents the point 3, and the shaded portion to the left of 3 represents the solutions to the inequality.
I hope this helps! Let me know if you have any further questions.