got a
today's lesson is about solving equations it is common corn under 12
standard
a point re: half-point morning today we're gonna learn about linear equations
and we're gonna solve them with one-step equations
in multi-step equations now to be successful in this lesson we need to
talk about some vocabulary
a variable is a letter or symbol used in place at the number
usually unknown a term is a number variable
heard the product of one or more numbers or variables
a coefficient is a number that is multiplied by a variable
a constant is a term that does not include a variable
a number only and equation is a number sentence containing
an equal sign now here's some examples the beach one of those things
a variable an example would be like X why or tea
it's just a letter we put in place Aven and noun
a term would be a collection variables
and coefficients so like 5x
-2 XYZ T or four
now coefficient that is the number that's placed inferno be there one
variable
or set a variable step monomial term so the coefficients
in these cases would be five in -2
a constant is when a number stands alone such as
to ornate -7 numbers they do not have variables with them
an equation is something that has an equal sign so it could be things like
-2 X equals four or five times two equals 10
but these have equal signs so both up a more examples of equations
if we're given something like to expose three calls 15 book
the variable is not isolated it's not on the side by itself
so we still don't know what X's we have to solve this equation to find out what
taxes
but if you're given something like X equal 6 well
X has been isolated so you know in this equation
the value other X is six
let's look at this equation exploits 3
equals seven now we want to solve for x we wanna see what
X is so to get the plus three to the other side to
Ashleigh TX we must do it opposite
in the opposite and adding three is to subtract 3
now on the left side they're gonna cancel of of on the right side that's
gonna tell us
X equals 7 -3 which is four
now we have isolated the variable so we have solved
tracks on this example into having a number
added to axe now it's multiplied how do you get
really have something that's multiplied by axe will dip divided of what we do is
it opposite in the opposite a multiplying
is dividing so we're going to divide both sides before now on the left side
the fourth cancel of in your gonna get X equals
import e8 divided by four is 12 so now we know the value their ex
in this equalization is 12 let's do one more example up a one step equation
so on this when we have ext about about Bob equals 55 now we have to do the
opposite of whatever's with ex dis all for it and the opposite have dividing
that I've
is d'amato by by five remember on any question we can do whatever we need to
his long as we do the same thing double sides so since I need to multiply the
left him sad by five
also have to multiply the right hand side my fav
now on the left side the fobs can't a lot so we could exit polls
and DD five times five is 275 so
this is the value that X now let's work on a two-step equation
this commenter having something added or subtracted or
multiplier divided by axe we are both of those things going on
but there's an order that we go in to solve a problem like this
the first thing we're gonna do is any number added or subtracted
with ex we've got to get rid of it we've got to get it to the other side
so in this case that man is for we've got a deal with it
first am the opposite of subtracting forty get it to the other sad
is to add four now on the left side the poor scandal of
on the right side we've got a combined 17 plus four
and that gives us 21 now to solve 3x equals 21
well we'd got a deal with that 3 it's multiplied so divided of
we do the opposite a multiplication which is division
and remember on an equation you can do whatever you want
his long as you do the same thing to both sides so on the left side dividing
about 3.3 scandal of
on the right side dividing battery will 21 divided by three
is seven sold this is solved in the Value Index
is seven now let's look at a multi-step equations
another words this one's going to take more than two steps how do we do a
problem that looks like this
well with any question the first thing you have to deal with is the parentheses
so to get redid the parentheses when it's multiplied by a number out front
bike in this case to
we must distribute the two well to Tom's wise to wire
into Tom's the five is -10 now everything else
I just brought down now we collect
black terms so the two why in the negative 7y will give you
a negative fob why now the -10 I just brought it down
the -15 have brought it down now this looks like a two-step equation
so to get the -10 to the other side which is what we always have to deal
with first in the number
added or subtracted with our variable we're gonna had 10 double sides
on the left side the teens cancel of so we get -5 what
equals in -15 plus 10 is -5
now how do we deal with the negative fob y equals -5
what it's multiplied by negative are so divided that of
divide both sides by -5 Sun the left side it cancels often you really get why
equals
Inc -5 divided by -5
well that's one that is our solution for this multi step equations
so with the skills that we just practice what's next in algebra
all be solving literally questions solving absolute value equations
in using equations to solve problems such as finding a missing test score
if you know your average so we're actually going to use this
to solve real-world problems
good
the