Question

What is the simplified result of following the steps below in order? (1) add 5y to 2x (2) multiply the sum by 3 (3) subtract x + y from the product
a. 5x + 14y
b. 5x + 16y
c. 5x + 5y
d. 6x + 4y
e. 3x + 12y

Answer 1

1. Add 5y to 2x
2. Multiply the sum by 3
3. Subtract x+y from the product

We'll follow the directions step by step and see what we can get.

1. 5y + 2x : Adding. This creates the "sum"
2. 3(5y + 2x) : We multiply the entire thing, since it makes up the "sum"
3. 3(5y + 2x) - (x + y) : Due to the order of operations, we would do the product (multiplying) first, and then subtract the value.

So we're left with: 3(5y + 2x) - (x + y)

Now we can simplify this value with the order of operations.

3(5y + 2x) - (x + y)
(15y + 6x) - (x + y) : The - between these can also be interpreted as a -1. We can multiply this out to eliminate the necessity of the parenthesis. 
15y + 6x - x - y
15y - y + 6x - x : Rearrange for our sanity.
14y + 5x (or 5x + 14y) 
Option A