Question

You are planning to spend no less than $6,000 and no more than $10,000 on your landscaping project. Write an inequality that demonstrates how much money you will be willing to spend on the project.
How can I write an equation to fit this? $10,000=$6,000-n?

Answer 1

Let's first consider why $10,000=$6,000-n is wrong. It only has an equal sign, and if we subtract 6000 from both sides, we get n=4000, which is definitely not right; n could be 6001, or 10000, or 6789.

We need two inequality signs to express this.

What do we know?

n is greater than or equal to 6000

AND

n is less than or equal to 10000

We could write:

6000 <= n <= 1000

which is exactly that, or we could phrase it as "n is somewhere between or including 6000 through 10000" which I can write as
n is a member of [6000, 10000]