Question

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

Answer 1

The expression is written `2xx(x+9) = 7`

The solution is `x = -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:

`2xx(x+9)`

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

`2xx(x+9) = 7`

To solve it, you first multiply:

`2x + 18 = 7`

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

`2x = 7 - 18`

`2x = -11`

Finally, divide each side by 2:

`x = -11/2`

Answer 2

`-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(x+9)`. 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(x+9) = 7`

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

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

Divide both sides by two to get x: `x = -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 `7/2`.

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