Step by step
The question
Question: solve (3x − 1)/4, + 2 = (x + 3)/2.
1 Remove the fractions
The bottom numbers are 4 and 2.
To remove them all at once, we multiply by one number that every bottom goes into.
2 goes into 4: 2 times 2 is 4.
So 4 works for both.
We multiply every part by 4, not only the fractions.
Each whole side is times 4, so 2 is times 4 too.
We do it on both sides.
Why both sides?
The = sign means both sides are the same amount.
If we change only one side, they are not the same any more.
4 divided by 4 is 1.
The bottom is gone.
4 divided by 2 is 2.
We write the small 2.
The bottom is gone.
We write it again, without the crossed-out parts.
4 times 2 is 8.
No more fractions!
2 Open the brackets
The 2 in front of the bracket multiplies every part inside.
So we write 2 times each part.
A bracket with a plus or nothing in front can just be removed.
2 times x is 2x.
2 times 3 is 6.
3 Group like terms
Terms are the parts between the + and − signs.
Like terms are the same kind: same letters, same powers.
Plain numbers go together.
−1 + 8 = 7.
Now we have 3x + 7 = 2x + 6.
4 Get x on one side
There is x on both sides.
We want x on one side only.
The numbers in front of x are 2 and 3.
We remove the smaller one, 2x.
Then the x part that is left is plus.
A plus x part is easier to work with.
So we remove the 2x from the right side.
To remove 2x, we take away 2x.
We do it on both sides, so they stay equal.
2x and − 2x make zero.
Cross them out.
3x − 2x = x.
Now we have x + 7 = 6.
5 Remove the + 7
We want x by itself.
The + 7 is in the way.
To remove + 7, we take away 7.
We do it on both sides, so they stay equal.
+ 7 and − 7 make zero.
Cross them out.
6 − 7 = −1.
So x = −1!
6 Check
Let's check: put −1 in place of x.
First the left side.
Now the right side.
Both sides are 1.
So x = −1 is right!
Let's look back.
First: remove the fractions.
Then: open the brackets.
Then: group like terms.
Then: get x on one side.
Then: remove the + 7.
Last: check.