SOLUTION: If the Product of a number and -3 is reduced by 5, the result is 25 less than twice the opposite of the number . find the number

Question 244623: If the Product of a number and -3 is reduced by 5, the result is 25 less than twice the opposite of the number . find the number
Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
If the Product of a number and -3 is reduced by 5, the result is 25 less than twice the opposite of the number . find the number
the key to understanding this word problem is translating the words used to common math terms
what is the product? it means multiply
so let n= the number
-3*n
reduced by means subtract
-3*n-5
the result means equals
-3*n-5=25
less than means subtract 25 from something.
what is the something twice the opposite of the number
twice means multiply by 2
What is the opposite of a number?
Opposite number or additive inverse of any number n is a number which, if added to n, results in 0, the identity element of addition. The opposite number for n is written as -n. For example, -7 is opposite to 7, because -\!7 + 7 = 0. You can say that the opposite number of a number, is the negative version of the positive number.
so we take 2*-n and subtract 25
-3*n-5=2*-n-25
simplify
-3n-5=-2n-25
add 3n to both sides
-5=n-25
add 25 to both sides
20=n
now let's check it
20(-3)-5=2(-20)-25
-60-5=-40-25
-65=-65
ok checked
so the number is 20

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