# If 12 is added to half of a number, the result is one more than the original number. What is the original number?

May 23, 2017

$x = 22$

#### Explanation:

We can find the original number by setting up an equation. Let's call the number $x$.

$\frac{x}{2} + 12 = x + 1$

Half of a number $x$, added to $12$, is equal to $1$ more than the original number $x$. Now we can solve!

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

Here, we brought all terms with variables to one side, and all other terms on the other. Now we need to isolate the variable. Start by rewriting the terms on the left.

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

Now we can subtract them.

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

Divide out a $- 1$.

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

Now multiply both sides by $2$ to completely isolate the variable and get the solution.

$x = 22$