If the product of a number and -5 is increased by 6, the result is 2 less than 3 times the opposite of the number. What is the number?

Question

This question is confusing me, And I need some help with it.

Answer 1

-5n, the product of a number, n, and -5

-5n + 6, increased by 6

-5n + 6 =, the result is

-5n + 6 = 3(-n) _{3 times the opposite of the number} - 2 _{2 less than}

-5n + 6 = 3(-n) - 2

Questions?

Can you solve for n and answer?

Answer 2

OK Troy here we go.

Let the unknown number = X then the product of that number and -5 is -5X

Increasing this -5X by 6 means the new number is -5X + 6 which we will call equation 1 or the result

This result (-5X+6) is 2 less than 3 times the opposite of the number.

The opposite of a number is its reverse on the number line. So for the number X, the opposite is -X.

3 times -X = -3X

If we subtract 2 from the -3X we get -3X - 2

Why did we subtract 2 from the -3X? The -5X + 6 is 2 less than the -3X so if we subtract 2 from the -3X, we can set the -5X + 6 = -3X -2 or put another way if we were to add 2 to the -5X + 6 (because this number is 2 less than the -3X) then we can set -5X + 6 = -3X - 2

So now we have -5X + 6 = -3X - 2

Adding 3X to both sides we get -5X + 3X + 6 = -3X +3X - 2

-2X + 6 = -2

-2X = -2 - 6 or -2X = -8

X = 4

If you have any questions let me know