To solve the given equation,
we need to find the value of the variable
that satisfies the equation, or makes the equation true.
In order to do this, we need to isolate the variable
on one side of the equation.
Notice how this equation has a fraction,
and therefore, we will first clear the parentheses
and then clear the fractions from the equation,
by multiplying both sides of the equation
by the least common denominator.
So again, the first step is to clear
the parentheses on the left
by distributing three fourths.
Remember we can think of two as two over one.
Distributing three fourths times x is three fourths x
minus three fourths times two,
or three fourths times two over one,
is equal to six fourths.
And then we still have minus three equals three.
Now notice how we could simplify six fourths.
However, we are going to clear the fractions
from the equation by multiplying both sides
of the equation by the least common denominator
which we can see is equal to four.
So when we have fractions in an equation,
we need to decide whether we want to work
with the fractions in the equation,
and then isolate the variable,
or first clear the fractions from the equation,
and then isolate the variable.
Again on this video, we will be clearing the fractions
from the equation.
So for the next step,
we will multiply both sides of the equation by four.
And now let's go ahead and show
the three products on the left.
We have four times three fourths x
minus four times six fourths
minus four times three
equals on the right side, four times three.
Now determine each product.
With the products involving fractions,
let's write four as a fraction
with a denominator of one.
And now for the first product,
we will simplify out the common factors
between the numerators and denominators.
Notice how we have a common factor of four
between the numerator and denominator.
Four divided by four simplifies to one
in numerator and the denominator.
Notice now we just have one time three x
which is three x.
Then we have minus, again simplifying before multiplying,
four divided by four simplifies to one
in the numerator and denominator,
giving us just one times six,
and therefore we have minus six.
And then we have minus four times three,
which is minus 12, equals four times three
which is positive 12.
Notice by multiplying both sides of the equation
by the LCD, we now have an equivalent equation,
that no longer contains fractions.
So now, solving this equation,
the next step is to combine like terms on the left,
negative six minus 12 is negative 18.
The left side simplifies to three x minus 18 equals 12.
Next we add or subject to isolate the variable term.
To isolate three x, we undo minus 18
by adding 18 to both sides of the equation.
Simplifying, we now have three x
and then negative 18 plus 18 is zero,
giving us three x equals 12 plus 18 which is 30.
The last step is to multiply or divide
in order to isolate the variable.
And since three x means three times x,
to undo the multiplication, we divide both sides by three.
Simplifying, three divided by three simplifies to one.
One times x is x.
We have x equals thirty divided by three which is ten.
The solution to the equation is,
x equals 10.
Now let's go ahead and check this
by verifying if we substitute 10
for x into the original equation,
it will satisfy the equation.
Performing the substitution gives us three fourths
times the quantity 10 minus two, minus three equals three.
Now to evaluate the left side, on the calculator.
Notice how the left side
does simplify to three,
which gives us three equals three which is true,
verifying the solution is correct.
I hope you found this helpful.