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# One-step inequalities: -5c ≤ 15

In addition to solving the inequality, we'll graph the solution. Remember to swap if you mutiply both sides of the inequality by a negative number. Created by Sal Khan and Monterey Institute for Technology and Education.

Video transcript

Solve for c and
graph the solution. We have negative 5c is
less than or equal to 15. So negative 5c is less
than or equal to 15. I just rewrote it a
little bit bigger. So if we want to
solve for c, we just want to isolate the c
right over here, maybe on the left-hand side. It's right now being
multiplied by negative 5. So the best way to just have
a c on the left-hand side is we can multiply both
sides of this inequality by the inverse of negative
5, or by negative 1/5. So we want to multiply
negative 1/5 times negative 5c. And we also want to multiply
15 times negative 1/5. I'm just multiplying both
sides of the inequality by the inverse of negative 5,
because this will cancel out with the negative 5 and
leave me just with c. Now I didn't draw
the inequality here, because we have to remember,
if we multiply or divide both sides of an inequality
by a negative number, you have to flip the inequality. And we are doing that. We are multiplying both
sides by negative 1/5, which is the equivalent of dividing
both sides by negative 5. So we need to turn
this from a less than or equal to a
greater than or equal. And now we can
proceed solving for c. So negative 1/5 times
negative 5 is 1. So the left-hand
side is just going to be c is greater than or
equal to 15 times negative 1/5. That's the same thing as
15 divided by negative 5. And so that is negative 3. So our solution is c is greater
than or equal to negative 3. And let's graph it. So that is my number line. Let's say that is 0, negative
1, negative 2, negative 3. And then I could go above, 1, 2. And so c is greater than
or equal to negative 3. So it can be equal
to negative 3. So I'll fill that
in right over there. Let me do it in a
different color. So I'll fill it in
right over there. And then it's
greater than as well. So it's all of these values
I am filling in in green. And you can verify that it works
in the original inequality. Pick something that should work. Well, 0 should work. 0 is one of the numbers
that we filled in. Negative 5 times 0 is 0, which
is less than or equal to 15. It's less than 15. Now let's try a number
that's outside of it. And I haven't drawn it here. I could continue with the
number line in this direction. We would have a negative 4 here. Negative 4 should
not be included. And let's verify that
negative 4 doesn't work. Negative 4 times negative
5 is positive 20. And positive 20 is
not less than 15, so it's good that we did
not include negative 4. So this is our solution. And this is that
solution graphed. And I wanted to do that
in that other green color. Here you go. That's what it looks like.