## five times the sum of a number and 2 is eleven less than eight times the number?

Let x represent the number
5(x + 2) +11 = 8x

5x + 10 + 11 = 8x
5x + 10 + 11 = 8x
5x + 21 = 8x
21 = 3x
x = 7
by: ♥ɴוᴄᴏʟᴇ ɴɢᴜʏᴇɴ♥
on: 16th October 10

### 3 Responses to “five times the sum of a number and 2 is eleven less than eight times the number?”

1. ♥ɴוᴄᴏʟᴇ ɴɢᴜʏᴇɴ♥ says:

Let x represent the number
5(x + 2) +11 = 8x

5x + 10 + 11 = 8x
5x + 10 + 11 = 8x
5x + 21 = 8x
21 = 3x
x = 7

2. como says:

5 ( x + 2 ) = 8 x – 11
5x + 10 = 8x – 11
21 = 3x
x = 7

3. husoski says:

Let n be the number. Then translate English to algebra in steps:

“Five times the sum of a number and 2 is eleven less than eight times the number.”
“Five times the sum of a number and 2″ = “eleven less than eight times the number.”
5 * “the sum of a number and 2″ = “eleven less than eight times the number.”
5 * (“a number” + 2) = “eleven less than eight times the number.”
5 * (n + 1) = “eleven less than eight times the number.”

That’s the left side. There are two valid interpretations of the right side. I’ll give the obvious one first:

5 * (n + 1) = “eight times the number” – 11
5 * (n + 1) = (8 * “the number”) – 11
5 * (n + 1) = (8 * n) – 11

I’ve used * for multiplication. You can omit that, and don’t need the parentheses around 8*n:
5(n + 1) = 8n – 11

Nobody expects you to write that many lines for one little problem. Just get used to the idea of taking apart numerical statements in English and converting the pieces to math symbols. This is where most people have most of their problems with word problems.

I said two interpretations. You could also translate “eleven less than eight times the number” as

(8 – 11) * n

…but that’s not as likely because many people would add a comma in English: “eleven less than eight, times the number.”