Step by step
The question
Question: solve 0.2(x + 5) = 0.5x − 1.
1 Remove the decimals
Decimals are hard to work with.
Let's get rid of them.
0.2 has 1 digit after the point.
Times 10 moves the point 1 place to the right.
Then every number is a whole number.
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.
10 × 0.2(x + 5) = 2(x + 5).
10 × 0.5x = 5x.
10 × 1 = 10.
Write the answers.
No more decimals!
2 Open the brackets
The 2 in front of the bracket multiplies every part inside.
So we write 2 times each part.
2 times x is 2x.
2 times 5 is 10.
3 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 5.
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 left 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.
5x − 2x = 3x.
Now we have 10 = 3x − 10.
Let's swap the two sides, so x is on the left.
Both sides are the same amount, so we can swap them.
We want x by itself.
Two things are stuck to x: times 3 and − 10.
First x was times 3.
Then − 10.
To take them off, we go backwards.
First we remove the − 10.
Then the times 3.
4 Remove the − 10
To remove − 10, we add 10.
We do it on both sides, so they stay equal.
− 10 and + 10 make zero.
Cross them out.
10 + 10 = 20.
Now we have 3x = 20.
5 Remove the 3
3x means 3 times x.
We want just x.
To remove times 3, we divide by 3.
We do it on both sides, so they stay equal.
3 divided by 3 is 1.
So just x is left.
So x = 20/3!
6 Check
Let's check: put 20/3 in place of x.
First the left side.
Now the right side.
Both sides are 7/3.
So x = 20/3 is right!
7 Type it in
The answer box takes 5 characters.
20/3 has 4.
It fits.
We type 20/3.
Let's look back.
First: remove the decimals.
Then: open the brackets.
Then: get x on one side.
Then: remove the − 10.
Then: remove the 3.
Then: check.
Last: type it in.