Translating Algebraic Expressions?

Question

Okay so, I'm really confused. I don't know what the question is asking me to do... One of them is says "Fifteen times a number is decreased by fifteen. This result is then increased by two times the number. The result is negative 5 times the original number minus the opposite of ten" I'm so lost! Help please

Answer 1

Break it down piece by piece and write as you do.  Here, like this:

"Fifteen times a number"

Ok, I'll call my number Q, just because I'm tired of X.  So, I write 15Q, because that's "fifteen times a number".  Next:

"decreased by fifteen."  Um, ok.

15Q - 15   (right?  You see what I did there?)

"This result is then increased"

15Q - 15 +

"by two times the number."

15Q - 15 + 2Q

Now here it gets a little wonky.  I'm interpreting it like so:

"The result is"

15Q - 15 + 2Q =  (So, I'm seeing this as building an equation)

"negative 5 times the original number"

15Q - 15 + 2Q = -5Q

"minus the opposite of ten"

Here, recall that "opposite" simply refers to the one on the other side of 0.  So the opposite of 10 is -10.  The opposite of -4 is 4.  So watch closely:

15Q - 15 + 2Q = -5Q - (-10)

From here, you can solve for Q on your own.  :)

Hope this helps!

Answer 2

15n -15 + 2n = -5n - 10

22n = 5

n = 5/22

or

15n -15 + 2n = -5(n-10)

22n = 65

n = 65/22 = 2 21/22

the problem is slightly ambiguous