A number I am thinking of

Statement

I am thinking of a number. The number is $6$ more than its own half. What is the number?

Solution

Unknown. Let $x$ be the number we are looking for.

Equation. ”$6$ more than its own half” means the number equals its half increased by $6$: $x = \frac{x}{2} + 6.$ Move $\dfrac{x}{2}$ to the left: $x - \frac{x}{2} = 6 \implies \frac{x}{2} = 6 \implies x = 12.$ Check: half of $12$ is $6$, and $6+6=12$. Correct. $\boxed{x = 12}$