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## Two-step inequalities

## Video transcript

A popular R&B band recently
returned from a successful three-city tour where
they played to at least 120,000 people. My brain immediately says that's
greater than or equal to 120,000. If they had an audience of
45,000 in Mesa and another 33,000 in Denver, how
many people attended their show in Las Vegas? So let's say Las Vegas, I'll
just use l for Las Vegas. So the number of people who
attended their show in Las Vegas plus the number that
attended their show in Mesa, which is 45,000, plus the number
of people that attended their show in Denver, which is
33,000-- those are three cities right there, Las Vegas,
Mesa, and Denver-- that has to be at least 120,000 people. Or another way of interpreting
that is greater than or equal to 120,000. So to figure out how many people
attended their show in Las Vegas, we just solve for
l on this inequalty. So if we simplify this left-hand
side, we get the number of people in Las Vegas
plus-- what's 45,000 plus 33,000, that is 78,000-- 78,000
is going to be greater than or equal to 120,000. Now to isolate the l on the
left-hand side of the inequality, we can subtract
78,000 from both sides. So minus 78,000, minus 78,000
on the left-hand side, these cancel out. And we're just left with the
number of people who attended the show in Las Vegas is going
to be greater than or equal to 120,000 minus 78,000. So 120,000 minus 80,000 is
40,000, and it's going to be another 2,000. So the number of people who
attended Las Vegas is going to be greater than or equal
to 42,000 people. And we're done, that's it