# If x represents a number, then how do you write an expression for the sum of twice x with twice a number one larger than x?

Nov 3, 2016

$2 x + 2 \left(x + 1\right)$ is the direct translation.
This simplify's to $4 x + 2$.

#### Explanation:

Lets break this down.

We have the word "sum," which means there will be a $+$ sign.

something$+$something else

"Twice x" translates to $2 x$, so now we have:

$2 x +$something else.

Now for the tricky part. "A number one larger than $x$" is $x + 1$. Bet we want two of those. We can't just write "$2 \times$" in front of it because that would mean only the $x$ was multiplied. Instead, we write it as $2 \times \left(x + 1\right)$ or just $2 \left(x + 1\right)$.

So there we are! $2 x + 2 \left(x + 1\right)$.

If you want to simplify the expression, follow these steps:

Distribute:

$2 x + 2 \left(x + 1\right) \rightarrow 2 x + 2 x + 2$

Combine like terms:

$2 x + 2 x + 2 \rightarrow 4 x + 2$

Ta-daa!