Step by step
The question
Question: solve for x in ax + bx = c.
We treat the other letters like numbers.
ax + bx = c
1 Take x out
x is in every part.
So we take it out once, and write what is left in a bracket.
ab + ac = a(b + c)
So x times (a + b) is c.
x(a + b) = c
2 Remove the (a + b)
(a + b)x means (a + b) times x.
We want just x.
To remove times (a + b), we divide by (a + b).
We do it on both sides.
(a + b) divided by (a + b) is 1.
So just x is left.
So x = c/(a + b).
x = c(a + b)
3 Check
Let's check with numbers.
We pick a = 2, b = 3, c = 5.
Our answer gives x = 1.
x = 52 + 3 = 55 = 1
Now we put all the numbers into the start.
First the left side.
Left: (2)(1) + (3)(1) = 2 + 3 = 5
Now the right side.
Right: 5
Both sides are 5.
So our answer is right!
Both sides equal 5
Let's look back.
First: take x out.
Then: remove the (a + b).
Last: check.
Answer
x = c(a + b)