Step by step
The question
Question: solve 3y − 4 ≤ 11.
This is an inequality.
The sign means less than or equal to.
We want y by itself.
Two things are stuck to y: times 3 and − 4.
The − 4 is on the outside, so it comes off first.
Then the times 3.
1 Remove the − 4
To remove − 4, we add 4.
We do it on both sides.
Why both sides?
The sign compares the two sides.
If we change only one side, the answer can change.
− 4 and + 4 make zero.
Cross them out.
11 + 4 = 15.
Now we have 3y ≤ 15.
2 Remove the 3
3y means 3 times y.
We want just y.
To remove times 3, we divide by 3.
We do it on both sides, so the sign stays true.
3 divided by 3 is 1.
So just y is left.
15 divided by 3 is 5.
So y is less than or equal to 5.
3 Show it on a number line
Books also write the answer like this.
It is called interval notation.
A square bracket means the end is in, like the filled circle.
∞ means it goes on for ever.
4 Check
Let's test one number from the answer: 4.
We put it in place of y.
First the left side.
Now the right side.
8 is less than or equal to 11.
True!
So the answer works.
Let's look back.
First: remove the − 4.
Then: remove the 3.
Then: show it on a number line.
Last: check.