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# One-step inequality involving addition

One-Step Inequalities. Created by Sal Khan and Monterey Institute for Technology and Education.

Video transcript

Solve for x plus 8 is
less than or equal to 6 and graph the solution. So we have x plus 8 is
less than or equal to 6. So let's solve this
inequality for x. And the easiest way to isolate
an x on-- let's isolate on the left-hand side
since it's already there-- is to just
get rid of this 8. And the best way to get
rid of this positive 8 is to subtract 8 from both
sides So let's subtract 8 from both sides. That won't change the
direction of the inequality. So the left-hand side--
x plus 8 minus 8. And you're just left with an x. The right-hand side-- 6
minus 8 is negative 2. And we still have the
less than or equal. So we solved the inequality. We have x is less than
or equal to negative 2. So let's draw that
on a number line. So that's my number line. Let's stick 0 over here. Maybe if we go 1,
and then we could go negative 1,
negative 2, negative 3. And we could keep
going to the left. And we want all of
the x's that are less than or equal
to negative 2. Since it can be
equal to negative 2, we'll put a filled-in line
right here at negative 2, and all of the values
less than that. If it was just less than, if
there wasn't the equal sign, we would have an open dot. But since this is
less than or equal to, we've closed this dot. And then we want all of
the values below that. And you could just sample a
few and verify for yourself that they work. Based on this,
negative 3 should work. And if you took negative
3-- negative 3 plus 8 is 5, which is definitely
less than 6, so that works. And negative 1 shouldn't work. It's not included in
this set over here. So let's try that out. Negative 1 plus 8 is 7, which
is definitely not less than 6. So just sampling
some points, it seems like we've got the
right solution.