What do I do to figure out this problem:

3x + 8 = 26 + x

The first thing you need to do is understand what you’re looking for.
what a ’solution’ means, what it looks like, and how you even know
when you have it.     I’m not sure you’re there yet.

The ’answer’ or the ’solution’ to the problem is a number.   It’s the number
that ’x’ must be in order for that line at the top to be a true statement.   There’s
only one possibility.

To find it, you can do anything you want to either side of the problem, as long as
you do exactly the same thing to the other side too.   With that ability, here’s how
to ’figure out the problem’, and find the answer:

The original problem:      3x + 8 = 26 + x

Subtract 8 from each side:

3x = 18 + x

Subtract ’x’ from each side:

2x = 18

Divide each side by 2 :

x = 9.

That’s what the answer looks like, and that’s what the answer is.

’ 9 ’ is the ONLY number you can write in place of ’x’ in the problem,
and have the problem read true.

I’ll show you what I mean.   Let’s take the original problem

                   3x + 8 = 26 + x

and let’s write ’ 2 ’ wherever we see ’x’ :

3 (2) + 8 = 26 + 2

3 (2) means 3 times 2, and that’s 6.
So now we have

6 + 8 = 26 + 2

Do the addition on each side, and we have

14 = 28.

That’s nonsense.   14 is not equal to 28.  The reason that happened
is because we put the wrong number in place of ’x’.  When we put the
correct number in place of ’x’, the left side will be equal to the right side.
To ’figure out the problem’ means to find out what that number must be.
For this particular problem, it’s 9.

Most important rule in algebra, do what you did on one side to the other when simplifying equations
So using this rule ∧ just do exactly what is says. First subtract 8 from the side with the 3x and then subtract onto the 26. Now you have 3x =18 + x. Now just subtract x from the side with the 18 and then subtract it to the side with the 3x, getting 2x = 18, now just divide by 2 on both and get x = 9. That’s your answer