Video Transcript
A factory produces cans with weight
𝑥 grams. To control the production quality,
the cans are only allowed to be sold if the absolute value of 𝑥 minus 183 is less
than or equal to six. Determine the heaviest and the
lightest weight of a can that can be sold.
The company uses this inequality to
control the range of the weight that their cans can be. To find out the heaviest and the
lightest weights, we need to see either end of this range. And that means we’ll need to solve
for 𝑥.
When we’re dealing with absolute
value, we need to break this up into two separate inequalities. First, we’ll have the case when 𝑥
minus 183 is less than or equal to six. After that, we consider the
negative case, if the negative of 𝑥 minus 183 is less than or equal to six.
However, we’d rather multiply
through by negative one. The negative of negative is a
positive. We flip the sign, and then we have
negative six, which makes our second inequality 𝑥 minus 183 is greater than or
equal to negative six. To solve for 𝑥, we add 183 to both
sides of our inequality. And we get 𝑥 is less than or equal
to 189. When we add 183 to both sides of
our other inequality, we see that 𝑥 is greater than or equal to 177.
The upper limit of the weight is
going to be 189, while the lower end of the weight limit will be 177, which means
the heaviest can that can be sold is 189 grams and the lightest can is 177
grams.
