Five times a number is less than three times the same number. Find such an answer.

## Five times a number is less than three times the same number. Find such an answer.

# 3 Answers

Hi, Ana.

You can use any variable to represent the number; the most common are n or x.

So, five times a number can be written as 5x (because there is a number and a letter being multiplied, we don't even need a multiplication sign).

5x < 3x

To get the variables on the same side, you subtract 3x from each side.

5x - 3x < 3x - 3x

then you get: 2x < 0

Divide both sides by two:

2x / 2 < 0 / 2

then you get: x < 0

Since x is less than 0 (and not equal to), the answer would be all negative numbers.

Hope this helps!

Kathye P.

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.

When you think of a problem such as this 5x<3x you have to view the entire range of numbers. There is no positive number multiplied by 5 that is less than the same number multiplied by 3; however, if the variable which is the x is a negative number the equation becomes true, For instance:

5(-1)<3(-1)= -5<-3

## Comments

I like your answer, Kathye P. I think there might be a typo, though.

Just to clarify for Ana, when you say "Divide both sides by zero", do you mean "Divide both sides by two"?

Oops, yes. Thanks for the catch!

I corrected the typo. :-)

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