Step by step
The question
Question: solve (x + 1)/2 = x − 4.
1 Remove the fraction
The bottom number is 2.
Times 2 will remove it.
We multiply every part by 2.
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.
2 divided by 2 is 1.
Write what is left.
Do the multiplications.
No more fractions!
2 Open the brackets
A bracket with a plus or nothing in front can just be removed.
3 Get x on one side
There is x on both sides.
We want x on one side only.
So we remove the x from the left side.
To remove x, we take away x.
We do it on both sides, so they stay equal.
x and − x make zero.
Cross them out.
2x − x = x.
Now we have 1 = x − 8.
Let's swap the two sides, so x is on the left.
4 Remove the − 8
We want x by itself.
The − 8 is in the way.
To remove − 8, we add 8.
We do it on both sides, so they stay equal.
− 8 and + 8 make zero.
Cross them out.
1 + 8 = 9.
So x = 9!
5 Check
Let's check: put 9 in place of x.
First the left side.
Now the right side.
Both sides are 5.
So x = 9 is right!
Let's look back.
First: remove the fraction.
Then: open the brackets.
Then: get x on one side.
Then: remove the − 8.
Last: check.