Question

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

Answer 1

The number is `5`

Explanation:

Let's translate the sentence piece by piece:

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

So, the left hand side is `6(x+3) = 6x+18`

• `12` times the number `\to 12x`
• `12` less than `\to 12x-12`

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

We can write the equation

`6x+18=12x-12`

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

`6x-12x = -18-12`

`therefore -6x = -30`

`therefore x = (-30)/(-6)=5`