Step by step
The question
Question: if 2x − 3 = 5, what is 6 − 4x?
We want 6 − 4x.
Let's look for it inside the equation.
1 Compare the two
Look at 6 − 4x and 2x − 3.
We compare them part by part.
4 divided by 2 is 2.
So −4x is −2 times 2x.
6 divided by 3 is 2.
So 6 is −2 times (−3).
Every part of 6 − 4x is −2 times a part of 2x − 3.
2 Multiply by −2
So we multiply both sides by −2.
We do it on both sides, so they stay equal.
Times −2 goes to every part.
−2 times 5 is −10.
Careful!
Both sides are times −2.
5 becomes −10.
−2 times 2x is −4x.
−2 times −3 is 6.
So 6 − 4x = −10!
3 Check
Let's check the long way: first we find x.
We want x by itself.
Two things are stuck to x: times 2 and − 3.
First x was times 2.
Then − 3.
To take them off, we go backwards.
First we remove the − 3.
Then the times 2.
To remove − 3, we add 3.
We do it on both sides, so they stay equal.
− 3 and + 3 make zero.
Cross them out.
5 + 3 = 8.
Now we have 2x = 8.
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.
8 divided by 2 is 4.
So x = 4!
Then 6 − 4x is 6 − 4 × 4 = 6 − 16 = −10.
The same answer.
It works!
Let's look back.
First: compare the two.
Then: multiply by −2.
Last: check.