Step by step
The question
Question: solve 0.5x + 1.5 = 4.
There are four choices.
First we solve it, the normal way.
Then we pick.
1 Remove the decimals
Decimals are hard to work with.
Let's get rid of them.
0.5 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 × 0.5x = 5x.
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 5 and + 15.
First x was times 5.
Then + 15.
To take them off, we go backwards.
First we remove the + 15.
Then the times 5.
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 5x = 25.
3 Remove the 5
5x means 5 times x.
We want just x.
To remove times 5, we divide by 5.
We do it on both sides, so they stay equal.
5 divided by 5 is 1.
So just x is left.
25 divided by 5 is 5.
So x = 5!
4 Check
Let's check: put 5 in place of x.
We get 4, the same as the right side.
So x = 5 is right!
5 Pick the choice
Our answer is x = 5.
That is choice C.
6 Why not the others
A is 1.25.
Wrong: 4 − 1.5 = 2.5, then 2.5 × 0.5: multiplied instead of dividing.
B is 2.5.
Wrong: 4 − 1.5 = 2.5, then forgot to divide by 0.5.
D is 11.
Wrong: 4 + 1.5 = 5.5: added 1.5 instead of taking it away.
Let's look back.
First: remove the decimals.
Then: remove the + 15.
Then: remove the 5.
Then: check.
Then: pick the choice.
Last: why not the others.