# A number equals four less than three times the number ?

Mar 7, 2018

See below

#### Explanation:

To solve this problem, you can set up the equation $x = 3 x - 4$. Now, you must isolate the variable, or get it alone. To do this, you must add 4 to both sides.

$x + 4 = 3 x - 4 + 4$

You are now left with $x + 4 = 3 x$. But, since we need the variable $x$ by itself, you must now subtract x from both sides.

$x + 4 - x = 3 x - x$

Simplify that, and you get the equation $4 = 2 x$. Divide both sides by $2$ now, so that $x$ is alone.

$4 \div 2 = 2 x \div 2$

Mar 7, 2018

The number is 2

#### Explanation:

This sounds rather confusing, but writing it out into an equation will help a lot in solving it.

(written:) A number equals four less than 3 times the number
(equation:) $N = 3 N - 4$

Now let's isolate all parts with $N$ to one side so that we can solve it. Let's subtract $3 N$ from both sides.
$N - 3 N = \cancel{3 N} - \cancel{3 N} - 4$
$N - 3 N = - 4$
$- 2 N = - 4$

Now let's divide by 2.
$\frac{- 2 N}{2} = \frac{- 4}{2}$

$- N = - 2$

Since we have a negative sign on both sides, we can actually multiply them both by $- 1$ so that they will both be positive (remember that negative $\times$ negative $=$ positive ). This will not change their value, but it will help the answer be easier to understand.

$- N \times - 1 = - 2 \times - 1$

$N = 2$