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

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Answer 1 · 2018-03-26T06:20:11

See below.

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:

$\frac{x}{2}$ $x/2$

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

$2 x - 3$ $2x-3$

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:

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

And we solve for $x$ $x$ :

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

$\Rightarrow x = 2 (2 x - 3)$ $=>x=2(2x-3)$

$\Rightarrow x = 4 x - 6$ $=> x=4x-6$

$\Rightarrow - 3 x = - 6$ $=>-3x=-6$

$\Rightarrow x = 2$ $=> x=2$