Which graph represents the solutions to this inequality: 5n−3<3(n+1)
To represent the solutions to the inequality 5n−3<3(n+1), we need to graph the corresponding equation 5n−3=3(n+1) first.
5n−3=3(n+1)
5n−3=3n+3
2n=6
n=3
Now, let's test a value that is less than 3, such as n=2.
When n=2, the left side of the equation becomes:
5n-3=5(2)-3=7
The right side of the equation becomes:
3(n+1)=3(2+1)=9
Since 7 is less than 9, the inequality 5n−3<3(n+1) is true for n=2.
Next, let's test a value that is greater than 3, such as n=4.
When n=4, the left side of the equation becomes:
5n-3=5(4)-3=17
The right side of the equation becomes:
3(n+1)=3(4+1)=15
Since 17 is greater than 15, the inequality 5n−3<3(n+1) is false for n=4.
Therefore, the solutions to the inequality 5n−3<3(n+1) are all values less than 3.
The correct graph representing these solutions would be a number line with an open circle at 3 and an arrow pointing towards negative infinity.
The correct graph representing these solutions would be a number line with an open circle at 3 and an arrow pointing towards negative infinity.
is it going left or right?
I apologize for the confusion. The correct graph representing the solutions to the inequality 5n−3<3(n+1) would be a number line with an open circle at 3 and an arrow pointing towards the left, representing values less than 3.
To determine which graph represents the solutions to the inequality 5n - 3 < 3(n + 1), we first need to simplify the inequality:
5n - 3 < 3n + 3
Next, we can combine like terms:
5n - 3n < 3 + 3
2n < 6
Divide both sides of the inequality by 2:
n < 3
Since the inequality has a less than (<) symbol, the solutions are all values of n that are less than 3. This means that n can be any number less than 3, but not 3 itself.
Therefore, the graph that represents the solutions to this inequality is an open circle at 3 on a number line, with an arrow pointing to the left towards negative infinity.