What is twice the sum of a number and 5

Question

Translating verbal Phrases 

Answer 1

The sum results from addition.

 

n + 5

 

Twice that would be...

 

2(n + 5)

Answer 2

By twice, we mean you add it twice, or ×2. 

So we're multiplying by 2, a sum between these two things 

1. A number that we do not know, so we'll call it x
2. The number 5

So the sum between x & 5 is simply x + 5, and we're multiplying that by 2.

So we're not doing 2x + 5, nor are we doing x + 2×5, because neither of those is "twice the sum" as the question states.

We do 2(x + 5). This tells us that whatever x + 5 turns out to be, we make twice that; and if we were to plug in a number for x, Order of Operations tells us to find the sum before we multiply by two.

 

Hope this helps,

Frank