-
- [Voiceover] Carly tried to
solve an equation step by step.
-
And they tell us, they see, we see
-
how she tried to solve the equation.
-
They say find Carly's mistake.
-
So let's see what Carly did.
-
She started with 7a = 28.
-
Then on the left hand
side she divides it by a
-
and on the right hand
side she divides by 7.
-
Well this seems strange.
-
When you're manipulating an equation
-
whatever you do to one
side, you have to do
-
to the other side.
-
Over here she decides to
divide the left side by a,
-
on the right side she
should divide by a as well.
-
Or if she wants to divide
the right side by 7,
-
she should divide the
left side by 7 as well,
-
but she's dividing both sides
by two different things.
-
So step 1 is where she makes the mistake.
-
The right thing for her to do,
-
or I guess maybe the
most reasonable thing,
-
if she wants to solve for
a, divide both sides by 7.
-
Then she would have
been left with just an a
-
on the left hand side,
because it would have been
-
7a/7 and a 4 over there.
-
She would have said, oh,
a must be equal to 4.
-
So let's keep going.
-
Let's do a few more of these.
-
Trent tried to solve an
equation step by step.
-
All right. Find Trent's mistake.
-
So a lot of mistakes happening
-
in algebra problems right now.
-
So g/3 = 4/3.
-
Now let's see. The first step.
-
g/3 x 3, so he's multiplying
the left hand side times 3
-
and on the right hand side,
he's multiplying by 1/3.
-
So once again, he's doing
two different things
-
to the left and the right hand side
-
even though you're supposed
to do the same thing.
-
If you do two different
things, the equality
-
will not hold anymore.
-
Notice, if these two things are...
-
If g/3 = 4, if you multiply this times 3
-
and you only multiply this times 1/3,
-
well then this thing is
going to become larger,
-
because is you multiply by
3 that's going to be larger
-
if you take the same thing
and multiply it by 1/3.
-
Then the equality won't hold true anymore.
-
In order for it to hold true,
if you're going to multiply
-
the left by 3 you have to
multiply the right by 3.
-
So he made a mistake on step 1.
-
All right.
-
Ling tried to solve an
equation step by step.
-
All right. Find Ling's mistake.
-
Let's see 12 = p + 6.2.
-
All right. So now it looks like,
-
on the left hand side Ling adds 6.2
-
and on the right hand side, so there was
-
p + 6.2 is the old right hand side,
-
but it looks they then
try to subtract 6.2.
-
So it's the same number, but over here
-
they're adding it and over
here they're subtracting it.
-
So they're not doing the
same thing to both sides.
-
If you want to add 6.2
to the left hand side
-
you need to add 6.2 to
the right hand side.
-
If you want to subtract 6.2
from the right hand side
-
you have to subtract 6.2
from the left hand side.
-
So a lot of mistakes going on in step 1.
-
Let me see one where there's
not a mistake in step 1.
-
All right.
-
Alanna tried to solve an
equation step by step.
-
4c = 12, divides the left hand side by 4
-
and then multiplies the
right hand side by 4.
-
No if you're going to divide
the left hand side by 4
-
you have to divide the right
hand side by 4 as well.
-
You don't multiply it by 4.
-
So a mistake in step 1.
-
Let's do one more of these.
-
All right. n + 12 = 18.3.
-
So over here you had n + 12
-
and then Rico subtracts 12.
-
So if he subtracts 12
from the left hand side
-
he needs to subtract 12
from the right hand side.
-
It looks like he does that.
-
He had 18.3 and he subtracts 12.
-
So he subtracts 12 from both sides.
-
So the left side is now
n + 12 - 12, was just n,
-
which is why he subtracted 12,
-
so you're just left with
an n on the left hand side,
-
and on the right hand
side, let's see, 18.3 -12.
-
Well 18 - 12 is 6, so this should be 6.3.
-
So he made a little bit
of an arithmetic mistake
-
in step, he made an arithmetic mistake
-
and I think we are all done.