# What is Twice the sum of a number and 9 is equal to 7?

Oct 6, 2017

The expression is written $2 \times \left(x + 9\right) = 7$

The solution is $x = - \frac{11}{2}$

#### Explanation:

This means you are to choose a variable to represent the "number". I will use "x"

The sum of a number and 9 is

$x + 9$

Twice the sum of a number and 9 would be:

$2 \times \left(x + 9\right)$

Now so far, this is only called an algebraic expression because while it contains a variable, it has not be made into an equation because it is not set equal to anything.

It becomes an equation when we note it is "equal to 7". Now, we write

$2 \times \left(x + 9\right) = 7$

To solve it, you first multiply:

$2 x + 18 = 7$

Now "isolate the variable" by subtracting 18 from each side:

$2 x = 7 - 18$

$2 x = - 11$

Finally, divide each side by 2:

$x = - \frac{11}{2}$

Oct 6, 2017

$- \frac{11}{2}$

#### Explanation:

Let's make "the sum of a number" a variable, let's say $x$. Now, all we have to do is translate from English into Math. Let's break this down:

English >> First part of the question - "What is twice the sum of a number and 9".

Math >> We know that our unknown number is some variable $x$. We also know that sum of a number $x$ and 9 is nothing more than $x + 9$. Lastly, we must take twice of this sum, so we're left with $2 \left(x + 9\right)$. Keep in mind, I used a set of parenthesis because the entire sum ($x + 9$) is being multiplied by two and not just $x$ or $9$.

English >> Second part of the question - "Is equal to 7".

Math >> Whenever you see "is" in a word problem, that almost always means "$=$". So if something is equal to $7$, it pretty much means "$= 7$".

Now, all we have to do is piece together both parts, which leaves us with: $2 \left(x + 9\right) = 7$

Open the parenthesis: $2 x + 18 = 7$

Move 18 over to the other side: $2 x = - 11$

Divide both sides by two to get x: $x = - \frac{11}{2}$

We can test whether or not we got the correct answer by manipulating this number like the word problem asked us to.

Taking this number and adding $9$, we get $\frac{7}{2}$.

Multiplying this number by two should then give us $7$, which in this case, it does. This means we solved the problem!