Welcome to another video
on solving two step equations.
This video will deal with two step equations with fractions.
Remember when solving a two step linear equation,
the goal is to isolate the variable on one side
of the equation.
We'll do this by first adding or subtracting
in order to isolate the variable term.
And then we'll multiply or divide in order
to isolate or solve for the variable.
And then step three, we should check our answers.
It is important to remember
that in order to maintain equality,
we must perform the same operation
on both sides of the equation.
So number one, we have two x plus 1/4 equals 3/5.
The variable is on the left side of the equation
so our ultimate goal is to have x equals
some numerical value.
So in order to isolate the variable here,
we have to undo this two and undo this 1/4.
We have to ask ourselves, which one can we get rid of
by adding or subtracting?
Well the opposite of plus 1/4 is minus 1/4.
So we're going to have to subtract 1/4 on both sides
of the equation to start with.
So we'll subtract 1/4 here and subtract 1/4 here.
Plus 1/4 minus 1/4, that's zero.
So we have two x on the left equals.
Here we're going to have to get a common denominator,
that's going to be 20.
So multiply this by four over four,
that will give us 20.
Multiply this by five over five,
that will give us 20 in the denominator.
So we're going to have 12/20 minus 5/20,
so we're going to have two x equals this will be 7/20.
And here we have to be a little bit careful.
This is attached by multiplication,
so the opposite of multiplying by two
would be dividing by two.
The problem is, this is in fraction form over here.
So instead of dividing by two,
it might be helpful if we multiply by the reciprocal.
So dividing by 2/1 is the same as multiplying by 1/2.
Notice when we do this, this is lined up nicely
on the right side.
On the left side, this simplifies nicely as well.
This two simplifies out,
so we have one x, or just x.
And on the right side, nothing really simplifies here
so we can multiply across the top
that'll be seven over 20 times two, so 7/40
would be our solution.
Let's go ahead and try another one.
Here we have 2/5 x minus 1/2 equals 3/5.
Again the variable is on the right side,
so our ultimate goal is to have x equals
some numerical value.
And we could undo the minus 1/2 if we add 1/2 on both sides,
that's going to be our first step.
This 2/5 is attached by multiplication,
so we'll have to undo that in the second step.
So again, to undo the minus 1/2,
we'll add 1/2 on both sides.
So this would be zero, that's why we did that.
So we have 2/5 x equals,
here we have to have a common denominator.
So it's going to be 10.
Multiply this by 2/2.
Multiply this by 5/5.
Notice both the denominators are now 10.
We're going to have 6/10 plus 5/10.
So let's go ahead and write this again.
We have 2/5 x equals 11/10.
This 2/5 is attached by multiplication,
but again instead of dividing by 2/5,
we're going to multiply by the reciprocal.
So multiply both sides by 5/2.
The left side simplifies perfectly.
We're left with one x, or x.
On the right side, the five and the ten simplify.
This would be one, this would be two.
Looks like we have 11/4.
This is perfectly fine for an answer
and is correct, but it is an improper fraction.
We could convert this to a mixed number
by taking eleven and dividing by four.
There are two fours in eleven,
that would be eight with a remainder of three.
That tells us 11/4 is equivalent to two and 3/4.
Either answer is correct and in simplest form,
just ones improper and ones a mixed number.
Number three, we have 1/4 equals 3/5 x minus five.
Now our variable is on the right side,
so that means when we get done we're going to have
some number equals x on the right.
So looking at the right side,
which can we undo by adding or subtracting?
We could undo minus five,
by performing the opposite operation or adding five.
So we'll add five to both sides of the equation.
So we'll add five on the right,
and we'll add five on the left.
But when I put plus five on the left,
I'm going to put plus 5/1
because I am going to have to get a common denominator here.
So the common denominator here is going to be four.
So I'll multiply this by 4/4.
So the left we're going to have 1/4 plus 20/4 equals.
We'll have 3/5 x
and then minus five plus five that's zero,
that's why we did that.
Let's go ahead and write this again.
Notice I am showing quite a few steps,
but if it helps me get the correct answer
I would rather show more steps than less.
So to isolate x, we have 3/5 times x,
so we could divide by 3/5
but instead we'll multiply by the reciprocal.
Or multiply by 5/3 on both sides.
Let's take a look at the left side.
This simplifies here, there's one three in three
and seven threes in 21.
That looks like that's about it.
So on the left, we have 35/4.
And on the right, again these are reciprocal.
So 5/5 and 3/3, that would all be one x or just x.
This is our solution.
And again it is an improper fraction.
Let's go ahead and practice converting it
to a mixed number.
35 divided by four, that's going to go in eight times
with a remainder of three.
This is equivalent to eight and 3/4.