anonymous
  • anonymous
5+3[1+2(2x-3]=6(x+5)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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sandra
  • sandra
I'm assuming you mean 5+3(1+2(2x-3)) = 6(x+5)
sandra
  • sandra
this is another case where you need to distribute
sandra
  • sandra
start with the right side, what is 6(x+5) ?

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anonymous
  • anonymous
yes
anonymous
  • anonymous
6x+30?
sandra
  • sandra
yep!
sandra
  • sandra
ok now start from the inside out on the left hand side
anonymous
  • anonymous
do u always start with the right side
sandra
  • sandra
so what is 2(2x-3)
sandra
  • sandra
well, I think generally start from inside out
sandra
  • sandra
as in inner-most thing that needs to be expanded
anonymous
  • anonymous
4x-6
sandra
  • sandra
ok great, so to recap, so far we have: 5 + 3(1 + 4x - 6) = 6x + 30
anonymous
  • anonymous
gotcha
sandra
  • sandra
so to make it easier on yourself, how about combing like terms in the parens, so what is (1+4x - 6) ?
anonymous
  • anonymous
5x-6 or do u break that down further
sandra
  • sandra
well, that's not correct
sandra
  • sandra
you can't combine 1 and 4x, since you don't know what 4x
sandra
  • sandra
but you can combine 1 and -6
sandra
  • sandra
(by adding them)
anonymous
  • anonymous
-5
sandra
  • sandra
if it had been (1x +4x -6) you would have been correct, since the 1 and 4 are both x's
sandra
  • sandra
right so the middle is now -5 + 4x, or 4x - 5
sandra
  • sandra
so now you have : 5 + 3(4x - 5) = 6x + 30
sandra
  • sandra
what is your next step?
anonymous
  • anonymous
5+12x-15=6x+30
sandra
  • sandra
great =)
sandra
  • sandra
so can you combine anything on the left side?
anonymous
  • anonymous
5 and 15 which is -10
sandra
  • sandra
yep =), so now what do you have?
anonymous
  • anonymous
is it 12x-10=6x+30
sandra
  • sandra
exactly
sandra
  • sandra
so now the basic rule of algebra, and equations/equalities in general - you can perform any operation to both sides of an equation and still have the equatoin be true (satisfied)
sandra
  • sandra
the reason that's powerful is because it allows you to eventually get x all by itself
sandra
  • sandra
so let's say you wanted to get 12x by itself on the left hand side
sandra
  • sandra
what could you add to both sides to make that happen?
anonymous
  • anonymous
add 10
sandra
  • sandra
yep, and what do you get if you add 10 to both sides
anonymous
  • anonymous
12x=6x+40
sandra
  • sandra
exactly. ok , so remember, when you're solving for a variable (in this case x), the idea is to get all of that variable to one side, and then eventually just one instance of that variable by itself (x)
sandra
  • sandra
so what could you subtract from both sides, to get all of the x's in one place?
anonymous
  • anonymous
would u minus 6x
sandra
  • sandra
exactly, and then what you get?
anonymous
  • anonymous
6x=40 then i divided by 6 both sides
sandra
  • sandra
yep!
sandra
  • sandra
good work
anonymous
  • anonymous
6.6?
sandra
  • sandra
yeah, or you could write it as a fraction
sandra
  • sandra
so x = 40/6
sandra
  • sandra
and that can be reduced if you divide both top and bottom by 2
sandra
  • sandra
so x = 20/3
sandra
  • sandra
so now that you think x = 20/3
anonymous
  • anonymous
thank u so much i think im getting it sum what lol
sandra
  • sandra
you stick it back into the original equation (or just use 6.666666 to check in your calculator)
sandra
  • sandra
and if the equation is true, then you know you got it right
sandra
  • sandra
so for these types of problems, try expanding everything out first
sandra
  • sandra
and then just keep doing the same operations on both sides until you conveniently get all the x's (or whatever you're solving for) in one place
sandra
  • sandra
and then just get the value for one x by dividing
sandra
  • sandra
after a while, you'll start seeing some shortcuts if they're there
sandra
  • sandra
for example, if you had 3(x+3) = 12
sandra
  • sandra
you wouldn't *have* to expand first
sandra
  • sandra
you could just divide both sides by 3
sandra
  • sandra
to get x+3 = 4
sandra
  • sandra
and then subtract 3 from both sides to get x=1
sandra
  • sandra
but seeing that will come with practice
sandra
  • sandra
good luck!
anonymous
  • anonymous
oh ok thanks a bunch !!!!
sandra
  • sandra
yep np

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