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