Up next in 10
How To Solve Equations By Adding Or Subtracting
7 views
Feb 19, 2025
Section 4.3: Solving Equations by adding or subtracting In today's lesson we'll be learning how to solve equations that involve both the addition and subtraction property of equality. Chapters: 00:00 Introduction 01:24 What is an equation 03:06 How to solve an equation by adding 13:21 How to solve and equation by subtracting
View Video Transcript
0:00
we're going to start a new chapter and
0:01
we'll talk about solving equations right
0:04
now before I start I want to tell you
0:06
why we do this now I remember taking our
0:10
dogs to like uh to uh petm to like weigh
0:15
my dogs and then he he one of my dogs
0:18
doesn't like to get on the scale so he's
0:20
always like trying to like get away from
0:22
it so what we have to do is this we have
0:24
to stand on the scale together and I
0:26
have to pick him up but before I do that
0:27
I have to weigh myself first right and
0:29
then I weigh myself from my dog now how
0:32
do I find my dog's weight so you minus
0:37
your pound from the pound that you guys
0:39
got together minus right so that's
0:41
called what you just did is called an
0:43
equation right because you don't know
0:45
your dog's weight right now assume that
0:47
I am 168 lb right now assume that my dog
0:52
and I no my dog and I together are 168
0:55
right and I'm
0:57
120 right so how do I find my dog's
0:59
weight I'm going to write an equation
1:01
for that 120 + x = what 168 right so 40
1:07
right 48 and how you find it you did
1:09
what 168 take away 120 so this is
1:13
basically an equation you see how you
1:15
guys always ask me when am I ever going
1:17
to use this kind of stuff you use it
1:19
every day without even knowing it right
1:21
now by
1:22
definition what is an equation he an
1:26
equation by definition right official
1:29
word is a mathematical sentence that
1:33
contains an equal sign showing that two
1:36
expressions are equal that is called an
1:39
equation so that is the formal
1:41
definition of an equation it's a
1:42
mathematical sentence that contains an
1:44
equal sign showing that two expressions
1:47
are equal now we talk about Expressions
1:50
right we talk about Expressions this is
1:52
an expression and this is an expression
1:55
so when you have two expressions and
1:57
they are separated by an equal sign you
1:59
call that an equation all right two
2:03
expressions separated by an equal signs
2:05
are called an equation okay so that's an
2:09
equation now the
2:14
process the process of finding X or the
2:18
unknown is called solving an
2:22
equation right that's how you you solve
2:25
an equation now to solve an equation
2:28
there's there's like two process
2:30
actually four but today we only going to
2:32
look at two we're going to learn how to
2:34
solve equations by
2:35
adding and we also going to learn how to
2:37
solve equation by subtracting and then
2:40
probably on Thursday we going to learn
2:42
how to solve equation by multiplying and
2:44
then Friday possibly solving equation by
2:48
dividing right and then by next when we
2:51
come out from Thanksgiving we're going
2:53
to put all these things together when's
2:55
the test the test is tomorrow right so
2:58
now first
3:00
now we're going to learn how to solve an
3:01
equation by using the addition property
3:04
right it's called the
3:06
addition property of equality
3:11
hey so we have
3:13
x - 7 = to5 and this is an equation so
3:19
how do you solve this equation here what
3:23
you going to do
3:24
yeah you want to I can tell you how I
3:27
solve the equation all right
3:30
tell me how do you solve the equation I
3:32
always start by by rearranging the
3:35
equation okay so I would do
3:40
um or um I think what I did for this one
3:43
is I did
3:44
um what - 7
3:47
= so 7
3:50
+5 okay because addition is OPP subra
3:56
and 7 + is two two all right that's a
3:59
that's that's a good thing right that's
4:01
good that's how you're supposed to solve
4:02
it so to solve an equation by addition
4:06
what you do is you use your addition as
4:09
your tool to get the answer right I have
4:12
x - 7 = 5 what am I solving
4:16
for x x I'm solving for what x x is what
4:21
I want to find right so to find X I need
4:23
to get X by itself I need to isolate
4:26
that's the word that we use isolate the
4:28
X X need to be by itself so why needs to
4:30
move
4:32
then- 7 right so to get rid of the -7 I
4:36
have to find the opposite of7 is what +
4:40
7 right so I want to get rid of this I
4:43
want to solve for x so what I must do is
4:46
this I must add seven on both Sid cuz if
4:50
you do one thing on one side you have to
4:53
do it on the other
4:55
side right you're trying to get X by
4:58
itself so this is - 7 to get rid of the
5:01
seven and to send it to the left side so
5:03
I can combine it with the5 I have to add
5:08
it any questions on this is anybody
5:11
confused here yeah um so why are we
5:15
doing x + 7 = 7 + 7 we solving for x
5:22
right we want to find X that's what I
5:24
want to find right I want to find what
5:26
it is right hey
5:30
I'm not just talking in the
5:32
air or I could be out there just looking
5:34
and talking or praying I'm talking to
5:36
you guys so pay attention so x - 7 is =
5:40
to5 I want to get X by itself right so
5:44
my my brain has to think okay what needs
5:46
to move if I want to get X by itself
5:49
what needs to
5:50
move 7 so how do I move it I want to
5:53
shift this from this side to this side
5:55
so I must add because this I do the
5:58
opposite of the operation okay so I want
6:00
to get rid of the7 I have to add seven
6:04
right but the thing is this an equation
6:06
is something that move is is synced
6:09
which means if I do if I make a change
6:11
on one side I have to make that change
6:12
on the other side right so I'm adding
6:14
seven here so I can move it to this side
6:16
because I want to shift it so now you go
6:20
like this you draw your line right this
6:22
is going to cancel out because -7 + 7 is
6:26
what zero right7 + 7 is 0 so now x
6:32
equals what what's 5 + 7
6:35
125 + 7
6:39
um no positive two posi positive two
6:43
right you see how everything is coming
6:44
together this is why I was saying in the
6:47
beginning of the year you need to learn
6:48
your negative and your positive because
6:50
now we're getting down to equations okay
6:53
that's going to be super hard if you
6:55
don't know your science that's going to
6:57
be a big deal okay now here I have -14 =
7:02
y - 11 how do I solve for y what do I do
7:06
here somebody
7:09
else how do I solve why somebody else
7:12
you just talk Nora I want to get y by
7:14
itself so why needs to
7:17
move how do I move
7:21
it
7:23
11 and I also added here you see that
7:26
right excellent so I want to get rid of
7:29
negative 11 I have to add 11 so I don't
7:32
understand so how come 1 2
7:35
3 and four here you know writing
7:37
anything down so I'm assuming that you
7:40
understanding it right because if I ask
7:42
questions later if I don't want to hear
7:44
I a really getting what you were saying
7:46
cuz I'm going to ask questions you you
7:47
be right
7:49
now yeah why did you make the first one
7:53
M you did plus seven on that one but
7:56
then on the second you did plus 11 oh CU
7:59
I Just sh as you see I move the equation
8:02
now4 is here so4 is y = y - 11 right my
8:08
my variable is y I want to solve for y
8:11
right if I want to solve for y y needs
8:13
to move
8:15
the1 right so I must add 11 on on here
8:19
and I must add it on on the other side
8:22
okay so now this is going to cancel this
8:24
one right I get -14 + 11 that gives me
8:29
three right so we're going to spend a
8:31
little bit of time working on this
8:34
kind okay we're going to we're going to
8:36
spend some time working on these type of
8:38
equations and then we're going to move
8:40
on to like the subtraction in in a
8:41
couple of minutes but let's do a couple
8:43
more of these what if I had I'll let you
8:46
all do this
8:48
x - 3 = to
8:52
12 I want you to solve for x okay all
8:55
yall do it and then tell what you got x
8:57
- 3 = 12
9:10
so we want to find X right so what do we
9:14
do here de how' you solve it um you add
9:18
12 to three I 12 3 is a 12 right and you
9:22
add it on this side too cuz you want to
9:24
get rid of that right so now you get x
9:26
equals what 15 15
9:30
okay you want to get rid of it so you
9:32
have to add the three you have to do it
9:34
on both Sid this is really easy okay
9:37
excuse me no it's x - 3 it's x - 3 so
9:41
I'm adding three cuz I want to get rid
9:43
of that right -3 + 3 that's gone so now
9:46
you have 12 + 3 is 15 yes quick question
9:50
how do you know which one to add on both
9:52
sides okay that's a good question how do
9:54
you know which one to add on both sides
9:55
so here's what you do I'll show you the
9:58
key here right if I
10:00
have x - 9 = 7 uh let's say -3 right
10:06
what am I solving for x x so what needs
10:10
to move then plus now what needs to move
10:13
if I'm soling for X I want X to be by
10:15
itself so what needs to move n the what
10:19
it's minus 9 right so to to Move It I
10:22
have to do the opposite it's called the
10:24
additive inverse right I want to move
10:27
this because I want to XV by itself so
10:29
I'm going to add what 9 and
10:34
N that make sense now cuz this is what
10:37
you trying to move you want to get X by
10:39
itself so you have to use the opposite
10:41
because to get rid of the9 you have to
10:43
add nine to it
10:45
number yes right
10:49
yes quickly all right so that gives you
10:53
six now now do this you do this x - 11
11:00
= 20 so tell me how you solve this x -
11:04
11 =
11:06
-20 so
11:09
do 11 under the 11 okay
11:13
and
11:16
11 okay
11:19
[Music]
11:23
112 + 11 uhhuh is going to be positive
11:27
no it's not going positive sorry
11:32
no 20 22 no no -
11:36
[Music]
11:37
209 right 9 you have a -2 + 11 you have
11:43
20 holes you you fill up 11 holes you
11:46
still have N9 holes that's 9 right that
11:50
make sense
11:52
okay all right let's do a couple more
11:55
this is going to take a little bit of
11:56
practice right so what if you have X
12:01
uh minus no plus
12:04
minus
12:05
20 equals
12:08
to
12:10
-20 all right so how do you solve
12:13
this x - 20 = -20 AB how would you solve
12:24
this excuse
12:27
me um
12:32
okay why are you adding
12:34
20 why are you adding 20 why to cancel
12:38
out the that's right to cancel out the
12:40
negative that's do reasoning see that's
12:42
the kind of Step I want to hear he
12:44
understand why he wants to cancel out a
12:47
negative great answer right so this is
12:49
gone so now what do you have x = what
12:51
what's - 20 +
12:53
20 zero so X is zero that's simple see
12:57
that is good reasoning um adding 20
12:59
because I want to cancel out a negative
13:02
see this is how you need to process
13:04
things in your head like this is why
13:06
it's good to understand what you're
13:08
doing if you understand it it becomes
13:10
easy because you go well yeah I want to
13:12
get rid of -2 so therefore I'm going to
13:14
have to do what I'm going to add 20
13:16
right now with that reasoning let's move
13:18
on to subtraction of property
13:21
subtraction property of equality right I
13:23
have y + 10 = 23 now let's think to
13:26
ourselves what are we solving for right
13:29
y why so what do I do here what do I
13:31
need to do um
13:35
change-
13:38
10 there you go that's it same principle
13:41
right here we added now we should
13:43
subtract because in this case I want to
13:45
get rid of the positive 10 so I going to
13:47
do what subtract 10 right does that make
13:51
sense so here now I'm going to do take
13:53
away the 10 and take away the 10 so
13:56
notice how every time we use the
13:58
opposite oper ation right if it's adding
14:00
you subtrac if subtracting you do what
14:03
you add yeah it's like you have like a
14:05
th and then you have a mystery number of
14:08
color pencils in box you have like 10
14:10
color pencils and then you want to try
14:12
and get just the mystery number you to
14:15
take away that's right it's like a scale
14:17
you can use that you have to balance it
14:19
out right so now 10us 10 is gone right
14:24
so Y is equal to
14:26
what3 huh um
14:29
13 13 right positive now KY since you
14:34
are talking a lot this morning I feel
14:35
like you can help me X plus 6 = 3 so how
14:38
do I solve for x don't ask her you do
14:42
it so what do I need to get rid of here
14:45
the X no not the X plus I want to get
14:49
rid of the Y six I want to get X by
14:51
itself so how do I get rid of the
14:53
six no don't ask it how you do that we
14:56
just talked about it reason reason
14:59
right this is positive six I want this
15:02
to
15:03
move so what do you do you subtract the
15:07
six yeah right you subtract it because
15:10
you're trying to get rid of the six so
15:12
we have to take away six right and
15:14
remember we say when you do one thing on
15:16
one side you have to repeat it on the
15:18
other side so this is min - 6 right so
15:21
now you get Z No 3 - 6 is -2 -3 right
15:26
this is gone here right as why that you
15:29
pay attention now I'm going to give you
15:31
a couple of things to work on and we're
15:32
going to wrap this up real quick okay so
15:35
this is basically
#Mathematics