Hi,

In solving an equation you are allowed two types of operations

you can add the same amount to both sides of the equation, or
you can multiply each side of the equation by the same amount.

With your equation

\[2x + \sqrt 2 = 3x - 4 - 3 \sqrt 2\]

I would begin by adding $-2x$ to each side. This gives

\[2x + \sqrt 2 - 2x = 3x - 4 - 3 \sqrt 2 -2x\]

which simlifies to

\[ \sqrt 2 = x - 4 - 3 \sqrt 2 .\]

Now add $ 4 + 3 \sqrt 2$ to each side and simplify.

Penny