# The quotient of a number and 2 is the same as the difference of the number doubled and 3. What is the number?

Mar 26, 2018

See below.

#### Explanation:

The first thing we need to do is derive expressions from the given problem.

"The quotient of a number and 2", can be written as:

$\frac{x}{2}$

And "the difference of a number doubled and 3" as:

$2 x - 3$

In the problem, it states that both of these expressions have the same value.

Knowing this, we need only set these expressions equal to each other:

$\frac{x}{2} = 2 x - 3$

And we solve for$x$:

$\frac{x}{2} = 2 x - 3$

$\implies x = 2 \left(2 x - 3\right)$

$\implies x = 4 x - 6$

$\implies - 3 x = - 6$

$\implies x = 2$