I wonder if maybe you didn’t type the question exactly as it appears in your homework.
First, let’s solve it the way you have it.
“Five times a number is less than three times the same number”
Let n be any number.
Five times a number: 5n
three times the same number: 3n
is less than: <
We end up with the inequality:
5 n < 3 n
Subtract 3n from both sides.
2n < 0
Divide both sides by 2.
n < 0
You can also see that this makes from the problem. Only for negative numbers would 5 times the number be less than three times the number. For positive numbers, 5 times the number is always greater than 3 times the same number. For n = 0, 5n = 3n
I think you may have meant to ask:
“Five times a number is three less than the same number”
If so, this is an entirely different problem. That “is” means equal sign. On one side you have 5 times a number, or 5n. On the other side you have three less than a number, or n – 3. The equation is:
5 n = n – 3
Subtract n from both sides.
4n = -3
Divide both sides by 4.
n = -3/4
Recheck the problem you are working on and see which solution actually applies.