Step by step
The question
Question: solve x + 1.5 = 4.
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 × x = 10x.
10 × 1.5 = 15.
10 × 4 = 40.
Write the answers.
No more decimals!
We want x by itself.
Two things are stuck to x: times 10 and + 15.
The + 15 is on the outside, so it comes off first.
Then the times 10.
2 Remove the + 15
To remove + 15, we take away 15.
We do it on both sides, so they stay equal.
+ 15 and − 15 make zero.
Cross them out.
40 − 15 = 25.
Now we have 10x = 25.
3 Remove the 10
10x means 10 times x.
We want just x.
To remove times 10, we divide by 10.
We do it on both sides, so they stay equal.
10 divided by 10 is 1.
So just x is left.
25 divided by 10 is 2.5.
So x = 2.5!
4 Check
Let's check: put 2.5 in place of x.
We get 4, the same as the right side.
So x = 2.5 is right!
Let's look back.
First: remove the decimals.
Then: remove the + 15.
Then: remove the 10.
Last: check.