To solve the equation by working backward, we have to first enumerate what is happening in the equation:
[tex]\begin{gathered} 1.-\text{ x} \\ 2.-\text{ multiplied by -4} \\ 3.-\text{ add 6} \\ 4.-\text{ equals -42} \end{gathered}[/tex]
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:
[tex]-4x+6-6=-42-6[/tex]
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:
[tex]-4x=-48[/tex]
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:
[tex]-4x\cdot\frac{-1}{4}=-48\cdot\frac{-1}{4}[/tex]
Solving this we get:
[tex]x=12[/tex]
