Step by step
The question
Question: solve 0.3x − 1.2 = 0.1x.
1 Remove the decimals
Decimals are hard to work with.
Let's get rid of them.
We multiply every part by 10.
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.
Times 10 moves the point 1 place to the right.
10 × 0.3x = 3x.
10 × 1.2 = 12.
10 × 0.1x = x.
Write the answers.
No more decimals!
2 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 right 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.
3x − x = 2x.
Now we have 2x − 12 = 0.
We want x by itself.
Two things are stuck to x: times 2 and − 12.
The − 12 is on the outside, so it comes off first.
Then the times 2.
3 Remove the − 12
To remove − 12, we add 12.
We do it on both sides, so they stay equal.
− 12 and + 12 make zero.
Cross them out.
0 + 12 = 12.
Now we have 2x = 12.
4 Remove the 2
2x means 2 times x.
We want just x.
To remove times 2, we divide by 2.
We do it on both sides, so they stay equal.
2 divided by 2 is 1.
So just x is left.
12 divided by 2 is 6.
So x = 6!
5 Check
Let's check: put 6 in place of x.
First the left side.
Now the right side.
Both sides are 0.6.
So x = 6 is right!
Let's look back.
First: remove the decimals.
Then: get x on one side.
Then: remove the − 12.
Then: remove the 2.
Last: check.