Step by step
The question
Question: make x the subject of 5x + a = bx − 1.
The subject is the letter on its own: x on one side, everything else on the other.
Here x is in two places, so we must bring them together.
1 Get the x terms on one side
bx is on the right.
To remove it, we take away bx.
We do it on both sides, so they stay equal.
Careful!
Taking away bx is written − bx, on both sides.
bx and −bx cancel each other.
They make zero.
Now we have 5x + a − bx = −1.
a has no x.
To remove it from the left, we take away a.
We do it on both sides, so they stay equal.
a and −a cancel each other.
They make zero.
Now both x terms are on the left: 5x − bx = −1 − a.
So after step 1: we took away bx and took away a, and now we have 5x − bx = −1 − a.
2 Take x out
x is in every part.
So we take it out once, and write what is left in a bracket.
It is opening a bracket, backwards.
From 5x, 5 is left.
From −bx, −b is left.
So x times (5 − b) is −1 − a.
3 Remove the (5 − b)
x(5 − b) means x times (5 − b).
We want just x.
To remove times (5 − b), we divide by (5 − b).
We do it on both sides.
(5 − b) divided by (5 − b) is 1.
They cancel each other.
So just x is left.
So x = (−1 − a)/(5 − b).
4 Check
Let's check with numbers.
We pick small numbers that give a whole answer: a = 2, b = 6.
Our answer gives x = 3.
Now we put all the numbers into the question.
First the left side.
Now the right side.
Both sides are 17.
So our answer is right!
Let's look back.
First: get the x terms on one side.
Then: take x out.
Then: remove the (5 − b).
Last: check.