Video Transcript
Select the option that is
equivalent to 𝑎 plus seven is less than zero. (A) 𝑎 is greater than negative
seven. (B) 𝑎 is greater than or equal to
negative seven. (C) Negative seven is greater than
𝑎. Or (D) negative seven is greater
than or equal to 𝑎. (B) 𝑎 is greater than or equal to
negative seven. (C) Negative seven is greater than
𝑎. Or (D) negative seven is greater
than or equal to 𝑎.
First, we write down what we
know. 𝑎 plus seven is less than
zero. We can start to solve this problem
by isolating the 𝑎 variable. To do that, we subtract seven from
the left side of the inequality. And to maintain this true
inequality, that means we have to subtract seven from the right side of the
inequality. On the left, 𝑎 plus seven minus
seven equals 𝑎. And on the right, zero minus seven
equals negative seven. We’ve just found that 𝑎 is less
than negative seven. Now, at first glance, it doesn’t
look like we have 𝑎 is less than negative seven as an answer choice. To help us clear that up, let’s
consider this inequality on a number line.
We’re dealing with negative seven,
and 𝑎 has to be less than that. On a number line, less than
negative seven would be more negative values. And that would be an arrow pointing
to the left. We’re saying that 𝑎 has to be
found to the left of negative seven on a number line. Using that information, let’s go
back and visit our answer choices. Option (A) says that 𝑎 is greater
than negative seven. And that’s the opposite of what’s
true. Option (B) says that 𝑎 is greater
than or equal to negative seven. Again, that is not true, since 𝑎
has to be less than negative seven. Option (C) is an inequality that
says negative seven is greater than 𝑎.
If we look at negative seven on our
number line, it is always true that negative seven is greater than 𝑎. Negative seven is greater than 𝑎
because 𝑎 is less than negative seven, which makes option (C) an equivalent
statement to 𝑎 is less than negative seven. When we look at option (D), it says
that negative seven is greater than or equal to 𝑎. But because the inequalities we’re
dealing with are only less than and greater than, they don’t have an equal-to
component, which makes option (D) false.
