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## Algebra basics

# One-step inequality word problem

Inequalities are more than abstract concepts and exercises. They help solve real life problems. Here's an example. Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

- Isn't the limit $1000? So we can be equal to or less than $1000. Correct me if I'm wrong.(10 votes)
- I'm pretty sure it just says that because above it it already states that it has to be less than $1,000(1 vote)

- ? This is the most hardest unit for me so far(8 votes)
- most hardest isn't gramatically correct just fyi(1 vote)

- how would you write this sentence into an inequality:

"Gary watches at most 2 hours of television on a weekday"?(4 votes)- Hint: "at most 2 hours" means gary can't watch any more than 2 hours. Which inequality do you think would match that situation? Give it a try.(2 votes)

- i want to know how you figured that out because i am sooooo confused(4 votes)
- I don´t get it, isn´t the limit 1,000?(1 vote)
- The problem states "less than $1000", so you can't spend 1000.

This makes the inequality "<" instead of "<=".

Hope this helps.(2 votes)

- a basic question; whats a patio?(1 vote)
- I believe a patio is kind of like a porch.(1 vote)

- how do we know that 333 1/3 is equals to feet2?(1 vote)
- these make me so confused(1 vote)
- What is confusing? Have you gotten one-step equalities down well? One step inequalities is just an extension of one-step equalities with the caveat that If you divide or multiply by a negative, you have to flip the inequality sign.(1 vote)

- how do slove a problem of inequalities like this

3x+y>-4(1 vote) - I don't get two or one step equations. Any help?(1 vote)
- lets say that 10x+6<26

To do this, I have to subtract both sides by 6 to get 10x by it self. Then I get this

10x+6-6<26-6... and the 6s cancel eachother out so I get

10x<20...now I divide both sides by 10 to get the variable by it self

x<10...And so x is less than 10(1 vote)

## Video transcript

A contractor is purchasing
some stone tiles for a new patio. Each tile costs $3,
and he wants to spend less than $1,000. And it's less than $1,000, not
less than or equal to $1,000. The size of each tile
is one square foot. Write an inequality that
represents the number of tiles he can purchase with
a $1,000 limit. And then figure out how large
the stone patio can be. So let x be equal to the number
of tiles purchased. And so the cost of purchasing
x tiles, they're going to be $3 each, so it's
going to be 3x. So 3x is going to be the total
cost of purchasing the tiles. And he wants to spend
less than $1,000. 3x is how much he spends
if he buys x tiles. It has to be less than $1,000,
we say it right there. If it was less than or equal to,
we'd have a little equal sign right there. So if we want to solve for x,
how many tiles can he buy? We can divide both sides of
this inequality by 3. And because we're dividing or
multiplying-- you could imagine we're multiplying by
1/3 or dividing by 3 -- because this is a positive
number, we do not have to swap the inequality sign. So we are left with x is less
than 1,000 over three, which is 333 and 1/3. So he has to buy less than 333
and 1/3 tiles, that's how many tiles, and each tile
is one square foot. So if he can buy less than 333
and 1/3 tiles, then the patio also has to be less than 333
and 1/3 square feet. Feet squared, we could
say square feet. And we're done.