Video Transcript
Write an inequality to describe
the following and then solve it. Negative five times a number is
at least negative 45.
We’ll start by writing the
inequality. We’ve got negative five being
multiplied by some number, which we’ll represent with the variable 𝑥, at least
negative 45. We know the other side will
have a negative 45. But what symbol should “at
least” represent?
We need to consider if this
could be more, equal, or less. “At least” means it could be
equal, but it could not be less. “At least” could also mean
more. So it’s equal to or more
than. And mathematically, we would
represent that with a greater than or equal to symbol. If negative five times a number
is at least negative 45, then negative five 𝑥 is greater than or equal to
negative 45.
This is the first part of the
problem, but we’ll now need to try and solve for 𝑥. Since we’re dealing with an
inequality, it should immediately be on our radar that if we’re multiplying and
dividing with positive values, the sign stays the same. But if we’re multiplying or
dividing with a negative number, we have to flip the sign. 𝑥 is being multiplied by
negative five. And to get 𝑥 by itself, to
solve for 𝑥, we’ll need to divide both sides of the equation by negative
five. Since we are dividing by a
negative here, we must flip the inequality symbol. Negative five 𝑥 divided by
negative five equals 𝑥. The sign is flipped. And negative 45 divided by
negative five is nine. Negative five 𝑥 is greater
than or equal to negative 45. And that means 𝑥 is less than
or equal to nine.
