Video Transcript
Which of the following
inequalities is equivalent to negative four 𝑥 is less than or equal to negative
one? A) 𝑥 equals one-fourth. B) 𝑥 is greater than or equal
to one-fourth. C) 𝑥 is greater than or equal
to four. D) 𝑥 is less than or equal to
one-fourth. Or E) 𝑥 is less than
one-fourth.
Our inequality is negative four
𝑥 is less than or equal to negative one. And we want to rearrange this
equation so only 𝑥 is on the left side. Right now, 𝑥 is being
multiplied by negative four. To get 𝑥 by itself, we’ll need
to do the opposite. We’ll need to divide by
negative four. But if we do that on the left,
we know we need to do that on the right.
And all of a sudden, we should
be thinking we’re dividing by a negative and we’re working with
inequalities. And that means, in order for
this inequality to remain true, we need to flip the sign. Negative four 𝑥 divided by
negative four equals 𝑥. And negative one divided by
negative four equals one-fourth. And that means an equivalent
inequality would be 𝑥 is greater than or equal to one-fourth, which is option
B.
We can check and see if this is
true. We’ve just said that 𝑥 can be
anything that’s greater than or equal to one-fourth. We know that one is greater
than or equal to one-fourth. So if we take our original
inequality, negative four 𝑥 is less than or equal to negative one, and we plug
in one, we should get a true statement. Is negative four less than
negative one? Yes, that’s true, which means
that one is a correct solution for 𝑥.
When we’re working with
inequalities, I recommend checking your solutions, because what if you forgot to
flip the sign? If you forgot, you would get 𝑥
is less than or equal to one-fourth. If you did that, you could’ve
chosen something like negative one to check your solution. Negative one is less than
one-fourth. But when you plug that in,
negative four times negative one equals positive four. And positive four is not less
than negative one, which would’ve told you that you’ve done something wrong. And you need to go back and
check. In this case, 𝑥 must be
greater than or equal to one-fourth, which is option B.
