Question

A number decreased by 10 is 3 times the difference of the number and 2.?

Answer 1

Unknown number: `-12`

Explanation:

The key realization is that if we model our unknown number with the variable `x`, then we can essentially set up the following equation:

`x-10=3(x-2)`

This is saying the exact thing as "number decreased by 10 is 3 times the difference of the number and 2".

Let's distribute the `3` to the terms on the right side to get

`x-10=3x-6`

Adding `10` to both sides gives us

`x=3x+4`

Subtracting `3x` from both sides, we get

`-2x=4`

Lastly, we can divide both sides by `-2` to get

`x=-2`

This is our unknown number. Let's make sure this answer makes since:

`-2` decreased by `10` would be `color(blue)(-12)`. Is this the same as three times the difference of the number and `2`?

The difference of the number and `2` is the same as `-2-2`, which is `-4`. Three times this is indeed `color(blue)(-12)`.

This means `-2` is our number.

Hope this helps!