Step by step
The question
Question: solve 0.2x + 1 = 1.6.
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 × 0.2x = 2x.
10 × 1 = 10.
10 × 1.6 = 16.
Write the answers.
No more decimals!
We want x by itself.
Two things are stuck to x: times 2 and + 10.
The + 10 is on the outside, so it comes off first.
Then the times 2.
2 Remove the + 10
To remove + 10, we take away 10.
We do it on both sides, so they stay equal.
+ 10 and − 10 make zero.
Cross them out.
16 − 10 = 6.
Now we have 2x = 6.
3 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.
6 divided by 2 is 3.
So x = 3!
4 Check
Let's check: put 3 in place of x.
We get 1.6, the same as the right side.
So x = 3 is right!
Let's look back.
First: remove the decimals.
Then: remove the + 10.
Then: remove the 2.
Last: check.