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Hi! This is your teacher, Barbara Rademacher, and one of your colleagues sent me this question. I think it's a really
good question, so I decided to make a video of it. We're going to solve and graph the inequality that you see right here.
So let's begn...
I've got 37
minus - I'm going to distribute
the minus sign so I'll have -4X minus
five is less than or equal to - I'm going to distribute the :
2X plus 4...
+ X.
Now I have my first line. I'm going to combine my like terms on the left side and my like terms on the right side
just like I would do
if I were working on an equation.
So we'll have 37 - 5 is 32,
and bring down the -4x
and that's less than or equal to
2X plus X is 3X
plus 4.
Now if we were working on an equation and this is where...
um...inequalities are a little different from equations in that
you want to always put your variables
on the left side (of the inequality sign).
It makes graphing much
easier. You can still get the problem right if you put your variables on the right hand side but it
becomes much more difficult to decide
which way to point your arrow. OK so I always
put my variables on the left side
of the inequality, so that's what I'm going to do now.
I'm going to subtract 3X
from both sides of the inequality.
That will give me
32
-7X and it's very easy to make a mistake here.
Remember that minus 4X subtract 3X is really -4X plus -3X which is -7X.
That's less than or equal to 3X-3X gives you a zero and you bring down
the 4.
Now, I'm going to move my constant term, 32, over to the other constant term, 4,
and subtract
32. I'll subtract
32 from both sides
of this equation. That will leave me with
-7 X is less than
or equal to
-28
Of course you can do that with a calculator in a much more straightforward way. I'm just not taking time to drag out the calculator.
Alright, now comes the tricky part:
very different from an equation -
when I divide both sides of this inequality
by -seven, a negative number,
I have to flip the sign, I have to turn it around. So I will divide by -7 (on the left)
and I will divide by -7 (on the right) but I have to turn the sign around because I divided
by a negative number. On the left, the -7's cancel out leaving me with an X.
Then I have greater than or equal to -28 divided by -7
Which is positive
4.
OK let's try putting that answer
in here (the answer box).
OK we're gonna choose
greater than or equal to (for the middle box)
four (for the right box).
We're gonna see if that's right. Hold your breath.
Hoorah!
Now let's talk about the graph: The answer is B, by the way, but let's talk about
WHY.
Here's the number line with
Infinity (on the right)
negative infinity (on the left)
and here's zero in the middle,
and we've got four:
1, 2, 3, 4
Our answer tells us that X might equal 4, or might equal 5 or 6 or 7.
X might equal for 4.00001
X can equal any number to the right 4,
so I drop a bracket around 4
and then draw an arrow pointing
to the right.
So that definitely
is the answer B, and we use a bracket because this is greater than or equal to. Whenever you
have a line underneath the inequality sign, you use a bracket.
OK good luck doing this yourself
and have a good day.