# Six times the sum of a number and 3 is 12 less than 12 times the number. How do you find the number?

Jun 21, 2018

The number is $5$

#### Explanation:

Let's translate the sentence piece by piece:

• Six times... $\setminus \to 6 \setminus \times \ldots$
• The sum of a number and $3 \setminus \to x + 3$

So, the left hand side is $6 \left(x + 3\right) = 6 x + 18$

• $12$ times the number $\setminus \to 12 x$
• $12$ less than $\setminus \to 12 x - 12$

So, the right hand side is $12 x - 12$

We can write the equation

$6 x + 18 = 12 x - 12$

Bring all the $x$ terms on the left and the numeric terms on the right:

$6 x - 12 x = - 18 - 12$

$\therefore - 6 x = - 30$

$\therefore x = \frac{- 30}{- 6} = 5$