Question

-3(-8-__x)-6(x-7) = 18x+66fill in the blank

Answer 1

Given the equation:

`-3(-8-\boxdot x)-6(x-7)=18x+66`

Let the blank be represented by the letter y.

We can then rewrite the equation as:

`-3(-8-yx)-6(x-7)=18x+66`

First, we open the brackets on the left-hand side.

`\begin{gathered} 24+3yx-6x+42=18x+66 \\ 3yx-6x+24+42=18x+66 \\ (3y-6)x+66=18x+66 \end{gathered}`

Comparing both sides of the equation, we have that:

`\begin{gathered} (3y-6)x=18x \\ \implies3y-6=18 \\ \implies3y=18+6 \\ \implies3y=24 \\ \implies y=8 \end{gathered}`

Therefore, the number which will be used to fill the blank is 8.

That is:

`-3(-8-\boxed{8}x)-6(x-7)=18x+66`