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## One-step inequalities

## 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.