Step by step
The question
Question: solve 5 − 2x ≥ 1.
This is an inequality.
The sign means greater than or equal to.
We want x by itself.
Two things are stuck to x: times −2 and + 5.
The + 5 is on the outside, so it comes off first.
Then the times −2.
1 Remove the 5
To remove 5, we take away 5.
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.
5 and − 5 make zero.
Cross them out.
1 − 5 = −4.
Now we have −2x ≥ −4.
2 Remove the −2
−2x means −2 times x.
We want just x.
To remove times −2, we divide by −2.
We do it on both sides.
We divide by a negative number.
That turns the sign around.
Greater than or equal to becomes less than or equal to.
−2 divided by −2 is 1.
So just x is left.
−4 divided by −2 is 2.
So x is less than or equal to 2.
Careful!
Many people forget to turn the sign.
They get x ≥ 2.
But we divided by a negative number.
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: 1.
We put it in place of x.
First the left side.
Now the right side.
3 is greater than or equal to 1.
True!
So the answer works.
Let's look back.
First: remove the 5.
Then: remove the −2.
Then: show it on a number line.
Last: check.