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.

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?

jim · Answer

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]