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How to Solve Multi Step Equations and Inequalities ( part 1)
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Feb 19, 2025
In today’s class session , we’ll tackle the last section of chapter 5 and discuss solving multi step equations and inequalities. Chapters: 00:00 Introduction 00:29 Solving equations with parentheses 04:54 Solving inequalities with parentheses 08:23 Solving multi step equations 12:48 Working on additional problems
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0:00
so now we working with like multi-step
0:02
equations and inequalities okay these
0:05
like I said these are all like a
0:07
combination of everything that we've
0:09
been doing since the beginning of the
0:10
year right now we have a lot more than
0:13
just simple uh equations we have
0:16
multisteps so you going to have to apply
0:18
every skill that you've learned so far
0:22
okay so now the first type of equation
0:25
that we're going to have is the one with
0:27
parenthesis here right I have three
0:31
par x + 2 = 12 so how do you solve this
0:35
what do you
0:39
do Kenzie what do you do
0:42
here you want to solve this when I say
0:44
solve it right I I want to find what x
0:48
right but to find X I have to do
0:50
something first right so
0:57
you subtract can we subtract
1:01
no right we can't because the the the
1:04
number is connected to the parentheses
1:07
so what does that
1:08
imply multiplication right now you have
1:11
two ways to solve it you can divide both
1:14
Sid by what three right because guess
1:17
what three can go into 12 how many times
1:20
four times right what if it wasn't what
1:23
if it was another number the the the
1:25
obvious choice will be to do what
1:28
to distribute
1:30
right remember what we did in in chapter
1:33
3 we did
1:35
this right we're multiplying so we're
1:38
going to do 3 * X right plus what 3 * 2
1:43
remember we did that so we're going to
1:46
go 3 * X is what what's 3 *
1:49
x 3X and then we keep the sign in the
1:52
middle right and then 3 * 2 is 6 = to 12
1:59
right so you see what we did here so we
2:00
going to go 3 *
2:03
X we keep the sign in the middle plus 3
2:06
* 2 which is 6 okay and then now what we
2:10
do from
2:13
here
2:14
yeah yes do you want are we to subtract
2:18
six we subtract six all
2:21
right subtract six first we get 3x is
2:24
equal to 6 and then we divide by three
2:28
right this this is why we call this a
2:31
multi-step cuz it's not just
2:32
straightforward you have to go through a
2:34
couple of steps before you get the
2:36
answer does anybody have any trouble
2:38
understanding this
2:40
here do I have someone that does not get
2:42
it did you all get it can we can we try
2:46
one on your own now right so I want you
2:48
to try this on your own four parentheses
2:51
x + 3 =
2:58
20 for
3:30
right all right AB tell me what you
3:33
going to do right so how' you do
3:35
it um I uhhuh okay
3:41
4X uhhuh what' you
3:44
get
3:46
okay and then what and then you subtract
3:49
12 from
3:52
okay so we get 4X = 8 right and then
3:58
divide by four right
4:00
so we got x = 2 again like I said
4:02
there's another way you can do it right
4:04
you can quote unquote you can divide
4:06
both side by four to begin with you can
4:09
if you
4:10
want right you can divide both Sid by
4:12
four and then that makes it easy right I
4:16
could have done it this way where I can
4:17
divide both Sid by four to begin with
4:19
right so I'll get x + 3 = 5 and then
4:24
subtract three I get x = 2 so there's
4:27
multiple ways to solve a problem right
4:29
if this is this is easier for you can do
4:30
that too same way I can do this I can
4:33
divide both side by three and that way I
4:36
make it simple right and I have x + 2 =
4:38
to what 4 and I solve for x if you don't
4:41
get it that way just go the traditional
4:43
way if that works better for you right I
4:45
don't want to impose anything now now
4:48
we're going to do the same thing with
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inequalities right solving inequalities
4:53
with paresis so now I have four
4:55
parentheses x - 3 is greater than
4:58
6 so what do I do here you can use your
5:02
not if you want all right look Emily you
5:07
can use your notes you want to look a
5:08
not go ahead and do that that's fine but
5:10
I can't I just can't help I want you to
5:12
use your notes if you have any notes you
5:13
want to use go ahead and use it but I
5:16
can't I can't help you though so what am
5:18
I going to do here yeah um
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I Use the distributive
5:25
property so 4x - 5 4x - 12 right do you
5:30
see guys 4x - 12 because there a
5:33
negative in in in in between them right
5:35
so this time is not 4x + 12 or 4x - 12
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we have to make sure we distribute
5:41
properly okay all right and then what
5:45
then I add 12 both sides I add 12 both
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Sid okay so we got 4X is greater than 18
5:52
then divide four on each side right so
5:55
we have X is greater than 18 over 4 now
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do we leave it like this
6:00
what do we do we have to always do what
6:04
what's the key word simplify right
6:07
simplify so what goes into four that
6:09
goes into
6:10
18 two two so you left what then X is
6:14
greater
6:16
than 9 what 9 / two right 9 / two it
6:22
goes um two goes into 18 and two goes
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into four right and if you want to turn
6:28
this into a mixed fraction you can right
6:30
4 and2 four 4 and 1 and 1/2 right yeah
6:33
so this is also or 4 and 1 and 1/2 you
6:36
can do that too if you want right now I
6:38
want you to try this on your own here 4
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y - 3 is less than or equal to
6:53
72 so I think this was chapter what what
6:56
chapter was this um four
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chapter 4 I could check chapter
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4 I want somebody else here you just did
7:22
uh let me see yes so first thing we do
7:26
is four 4 y mhm is 12 mhm which is
7:33
greater is more than than this is no
7:36
more than what is it less less than or
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equal to equal to 72 all right so now we
7:42
have to add 12 add 12
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okay so Y is
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or uhhuh so now we divide four on both
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sides MH so that is y is less than oral
8:05
to 12 21 21 you meant to say 21 12 all
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right good uh so far so good right now
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I've not yet made it a little difficult
8:16
I wa in a second but now I do want us to
8:18
do do this as well right now we going to
8:20
learn how to solve multistep equations X
8:24
we have more steps here right so Alena
8:27
what do you think I'm going to do here I
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have four x + 5 = 3 2x + 4 use the
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distrib property Use the distributive
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property so what do I get on this
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side mhm plus 20 and on this
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side
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mhm + 12 right now we are here 4x + 20 =
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6X + 12 so now what is next what do you
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think
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all right like ter so how you going to
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do
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it can we add them up how do I move one
9:06
thing from one side to the other side so
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you want to take this one here right so
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because there's equal sign that separate
9:12
them I'm going to do what I'm going to
9:14
subtract right 6X and I'm going to
9:17
subtract 6X right because we can't add
9:20
them up because they're not on the same
9:22
side we have to since I want to move
9:24
this I want to put them together like
9:25
terms like you say so I have to subtract
9:27
it okay so now this is gone so that was
9:30
4x -
9:33
6X -2X right so we have -2x + 20 = to 12
9:38
now what is
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next subtract uh I want the numbers to
9:46
be on
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what the same side right so I'm going to
9:50
subtract what 20 right take away
9:55
20 I'm going to take away 20 here so I
9:58
have -2 x 12 - 20 that is 8 right and
10:04
then what's the last
10:06
step divide by
10:08
-2 right divide by -2 now we get x = 4
10:14
so if you go back you see so what I've
10:17
learned when I was in school is my
10:19
teachers always told me keep your
10:20
variable on the left side and then your
10:22
numbers on the right side now is it a
10:24
convention no is it it's not
10:26
conventional you can put the variables
10:28
on the right and numbers on the left I
10:30
don't care what you do right preferably
10:32
I like to keep my my variables on the
10:35
left side which is it's not that you
10:38
have to do it this way you can do it
10:39
however you want but it looks easier for
10:42
me when I keep them on the left side
10:43
right so now here you see what we did
10:45
here obviously we have to first
10:47
distribute the numbers and then combine
10:49
like terms like you said she said right
10:51
like terms now because 4X is here and 6X
10:55
is here if I want to put the x's on the
10:58
same side I have to subtract 6X okay
11:01
this is how you combine it now let's try
11:04
this you guys go ahead and try the uh
11:06
those two problems there question could
11:09
you do it the way where you um the multi
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step equations where you divide like the
11:16
four from each side yeah you you could
11:18
do that but guess what because you have
11:21
you going to have three4 you don't want
11:22
to do now if this number was eight that
11:24
would have been perfect right but
11:26
because this is three that's not going
11:28
to be so
11:29
easy to do right so here now we have 12x
11:33
+ 12 = 6 * 3x + 3 Vicki what do you do
11:36
here we have 12 x +
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12 =
11:41
to 6 and then 3x + 3 I'm trying to solve
11:45
this for X so what do I
11:48
do
11:50
subract can you subtract it right away
11:53
what do you have to do first you have to
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get rid of
11:58
what the parentheses right so how do you
12:01
get rid of it you have to distribute
12:03
this
12:05
first 3 * 3 so that what what 6 *
12:10
3x uh 18 18 x what's 6 * 3 again 18 18
12:16
now what are you going to
12:25
do what are you trying to do you're
12:27
trying to keep all the like terms
12:29
together right like terms you want to
12:31
keep them together so now we have 12x +
12:34
12 = 18x + 18 okay so what I want to do
12:40
is this like I said like two minutes ago
12:43
I want to keep all my variables on the
12:45
left side so I need to do what I want to
12:46
put the 12x and 18x together so that
12:50
means I'm going to do what to
12:51
this am I going to add it or subtract it
12:54
add I can't add subtract subtract it
12:57
right I have to sub any time you move it
12:59
you have to subtract it right you have
13:02
to subtract it right so this is gone now
13:06
you have what 12x - 18
13:11
x -6x right + 12 equal to 18 now what
13:17
now I want to do the same thing with the
13:18
numbers so which number do I need to
13:20
move the 12 or the
13:27
18 18 well if I move the 18 does that
13:30
help me no so it's easier to move what
13:34
12 so how do I move the
13:37
12 what how did you move the 18 here
13:40
subract subtract it right you subtract
13:43
it so now this is gone so you have
13:46
-6x = 6 now what I want to get X so
13:51
what's the my last
13:53
step divided by
13:56
what by6
14:00
-6 right so now we have x = -1 okay you
14:05
see how long the steps are this is
14:07
called this is why we call this a
14:08
multistep equation it's multistep so you
14:12
guys go ahead and try this on your own
14:13
five parentheses y - 3 = 3 is x + 7 okay
14:21
try this on your own and tell me what
14:22
you
14:28
got for
15:51
oh my gosh I'm so sorry guys I me wor
15:54
different yeah this has to be why I'm
15:56
sorry oh thank you this has to be y I'm
16:00
sorry guys I
16:02
apologize have two different variables
16:04
here yeah I was like so this is y
16:07
instead of X okay
16:09
sorry
16:22
yeah no no no don't WR yet you have 5 y
16:27
-
16:27
36 equals
16:30
to 3 y so you want to put all the Y's on
16:32
one side right since you have the number
16:34
on the left side you want to put the Y
16:36
on the right side so you have to
16:38
subtract
16:43
what 5
16:55
y all right good
17:12
good all right know going to happen cuz
17:14
she just finished her all right so what
17:16
did you do first um I distribute it so
17:20
it's 5 y - 15 is = 3 y plus 21 all right
17:25
is everybody on board with this one so
17:26
far right everybody got to this y - 15
17:29
all right and then um then you subtract
17:33
21 115 she subtract 21 so we have 15 -
17:38
21 which equal 36 so it's 5 y - 36 is =
17:44
3 y okay then you subtract 5 y all right
17:47
= 36 is = to -2 y then you subtract -2
17:52
you you mean divide or divide yeah yeah
17:55
wait can we do like could we have done
17:57
it like um do this multiple ways yeah
18:01
did you add
18:02
15 I I um I subtracted I
18:06
subtracted yes you can do that too yeah
18:09
you can do that that's fine you could
18:11
have also done it let me just take it
18:12
from here right many paths to
18:15
get there's many paths to solve this but
18:17
there's no many path to die right this
18:20
is this is we have to be careful so here
18:23
you subtracted 3 y right that's what you
18:25
did correct 3 y you going to get the
18:28
same exact thing right you got 2 y - 15
18:32
= 21 and then you added 15 all
18:36
right and then you have 2 y = 36 and
18:40
then you divide it by two right and you
18:43
got y = 18 so there so again there's
18:46
multiple ways you have to find what
18:48
works for you right I personally would
18:50
have done it this way because just like
18:53
you people hate this double netive right
18:56
I would have done it this way cuz I
18:57
don't like negatives and I don't like
19:00
fractions so you always want to make
19:01
your task easier now what we're going to
19:03
do is this now we're going to make it a
19:06
little hard right now we just so far
19:09
what we have is Basics going to give us
19:11
two different it gets harder than this
19:13
yes it gets a little harder than this
19:14
right so now we're going to do we did
19:16
the basics now let's move on and let's
19:19
do something a little bit harder than
19:20
that that was Basics that was kind of
19:23
Basics right now let's say we have we
19:25
have this here right let me give you
19:27
something where we have
19:29
-3 pares x -
19:33
7 = to uh 18 right now what is different
19:40
this time what do you see that is
19:41
different
19:42
here what did that do two negatives I
19:46
did negatives right because every single
19:49
problem we had positive so you made it
19:50
easier now we have negative signs so now
19:53
it could be complicated right yeah I
19:56
just have a question when you did give a
19:59
y and x that possible to solve no you
20:04
can only solve a two variable equation
20:06
if you have a system of two equations
20:08
like this if you go to Algebra 2 or
20:10
algebra one you're going to have
20:12
something like this maybe I quickly give
20:14
it to
20:17
you now you can solve it so it's called
20:20
a system of equation right we have two
20:22
varibles once you get to algebra one or
20:25
maybe Algebra 2 you're going to deal
20:27
with this kind of equation okay right
20:29
now we're not doing that yet okay you
20:31
guys are still in the basics so now we
20:34
have this here right it's a little bit
20:37
complicated because we have negatives
20:39
and this is where in this chapter I
20:41
remember when we was doing the
20:42
distribution the distributive law it
20:45
caused a little bit of problem right so
20:46
let me help you here so the first thing
20:48
I'm going to do is what -3 *
20:51
what
20:52
x right -3x right and then remember now
20:58
some of you guys did it differently
21:00
right now you have -3 *
21:04
what which
21:06
is 21 no not negative positive plus 21
21:12
right you see so now you have -3 * x-3x
21:16
-3 * + 21 or if you want if you don't
21:19
want to do it this way you can just go
21:21
let me show you something you just go
21:23
minus right -3 * 7 you can do it this
21:27
way too so that way
21:29
you know that you're not going to
21:30
confuse your sign if you're not that
21:31
fast
21:33
yes you got all right okay so we know
21:36
for a fact that we have -3x + 21 = 18
21:41
then what yes go ahead and tell me see
21:44
you got it yeah
21:47
so
21:49
subract
21:52
okay
21:56
SO3 = x = 1 right so you see again it
22:01
gots a little bit complicated because
22:03
you have double we have negative you
22:04
have negative so we have to be aware of
22:06
our signs this is why I was saying the
22:08
beginning of the year you have to get
22:11
the signs together you have to really
22:13
understand that right now let's let's do
22:15
the same thing with the other ones now
22:17
let's assume that I have
22:20
now
22:22
right -5 * x + 6 is more than
22:29
uh let's see negative uh 30 go ahead and
22:34
try to solve this for
22:35
me5 parenthesis x + 6 is greater than
22:50
-3 I take picture
22:52
my yeah
23:18
now whoever gets this problem right if
23:20
you can tell me I'll give you one extra
23:22
credit point if you get it right I give
23:25
you like two three minutes to finish it
23:26
so if you get it right where who I mean
23:29
whoever gets it right if you got the
23:31
right I'm going to come and check your
23:32
taable if you got it I'll give you one
23:34
ex whenever there's a positive negative
23:38
like say I did it but I'm not sure okay
23:41
wait a minute yeah wait this problem
23:43
here yeah if it's like plus 30 would you
23:46
be like adding 30
23:49
yeah are you finished there's no way you
23:52
finish this fast I did you
23:55
sure okay let me see
24:01
okay so far so
24:02
good oh all right then
24:06
what
24:08
mhm you're trying to solve for what x so
24:11
you have to do what mhm uh no divide I'm
24:16
dividing
24:24
okay you div by what you divid by what
24:28
so what has to
24:30
happen good all right so let me see
25:11
okay you good so far here now
25:35
just the sign all right just flip
25:38
it mhm yes I I've already seen you good
25:42
all right fig
25:48
[Music]
25:53
it good oh good I didn't think I didn't
25:57
think it was valid you good all right
26:00
all right good so after yeah yeah I got
26:03
yeah oh let me we get EX give me
26:08
ex you want wait or you want you want me
26:11
correct all right so all I'm actually
26:15
pleased with you guys you guys do pretty
26:16
good for the most part so most of you
26:18
guys -5x right - 30 is greater than -30
26:23
right and then plus
26:26
30 oh it's + 30 so you have -5x is
26:31
greater than zero and I think a lot of
26:32
you guys got told you w what yeah you
26:35
divide by5 right and when you divide by5
26:39
this does what flips so you have X is
26:43
less than zero so yeah so I have one two
26:47
hold on a second I even def fin so I
26:49
have the uh I have
26:56
what Dexter
26:59
Caleb and then that's it right anybody
27:03
else that it all right okay so good so I
27:09
see that you're getting comfortable with
27:11
this stuff so we need to keep moving
27:12
right so now what I'm doing is I'm
27:15
changing them so now I'm going to do the
27:16
same thing here I'm going to have -2 x -
27:21
6 is equal to uh let's say 10 and thenx
27:26
- + 2 plus one yes go ahead and solve
27:30
this is one yeah
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