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### Course: Operations and Algebraic Thinking 222-226 > Unit 2

Lesson 7: One-step inequalities- Plotting inequalities
- Inequality from graph
- Plotting inequalities
- Testing solutions to inequalities
- Testing solutions to inequalities
- One-step inequalities examples
- One-step inequalities: -5c ≤ 15
- One-step inequalities
- One-step inequality word problem
- One-step inequalities review

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# 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.(11 votes)
- I didn't understand what u tried it to say very well, but the problem states that has to be
**less**than 1000 not equal(3 votes)

- ? This is the most hardest unit for me so far(10 votes)
- how did you get 333 1/3 at1:35in the video(4 votes)
- you divide 1000 by 3(6 votes)

- i want to know how you figured that out because i am sooooo confused(4 votes)
- how would you write this sentence into an inequality:

"Gary watches at most 2 hours of television on a weekday"?(3 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)

- Does anyone know of a shop that would sell a third of a tile? Surely the correct answer is 333 tiles, 333 sq ft.(2 votes)
- i know, right? but you CAN ask for a third in most places(4 votes)

- a basic question; whats a patio?(1 vote)
- I believe a patio is kind of like a porch.(5 votes)

- shouldn't the patio be <= 333.3 sqft?(3 votes)
- I don´t get it, isn´t the limit 1,000?(0 votes)
- The problem states "less than $1000", so you can't spend 1000.

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

Hope this helps.(6 votes)

- why 1,000 tiles?0:45(2 votes)
- Actually he wants to spend less than $1000 dollars. Not 1000 tiles(2 votes)

## 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.