Question

Solve the following equations by working backward through the number trick.

Answer 1

To solve the equation by working backward, we have to first enumerate what is happening in the equation:

`\begin{gathered} 1.-\text{ x} \\ 2.-\text{ multiplied by -4} \\ 3.-\text{ add 6} \\ 4.-\text{ equals -42} \end{gathered}`

So first, we have to use the inverse operations to solve the equation; first we look at the bottom and start with "add 6". Since this is an addition, we are going to use substraction:

`-4x+6-6=-42-6`

Notice how I wrote -6 on both sides of the equation, this is because in this way you don't mess with the original value of x! (besides, it's like if you add a 0).

Doing the operations we get:

`-4x=-48`

On our next step we have that x is multiplied by -4, so that means that we have to divide both sides of the equation by 4, or, which is the same, multiply by -1/4:

`-4x\cdot(-1)/(4)=-48\cdot(-1)/(4)`

Solving this we get:

`x=12`