We want to solve the given equations.
For the first equation,
we have x divided by 5.1 equals 4.5.
The solution is the value of x
that satisfies the equation
or makes the equation true.
To solve the equation,
we need to isolate the variable on one side of the equation.
Notice right now on the left,
we have x divided by 5.1,
which means to solve for x,
we need to undo this division
by performing the opposite operation
to both sides of the equation.
To undo dividing by 5.1,
we multiply both sides of the equation by 5.1.
On the left side of the equation,
multiplying by 5.1 undoes dividing by 5.1.
If we want, we can write 5.1 as a fraction
with a denominator of one,
and notice now we have a common factor of 5.1
between the numerator and denominator.
Simplifying out the common factor of 5.1,
5.1 divided by a 5.1 simplifies to one in the numerator
and denominator,
leaving us with one times x, which is just x.
On the right, we have 5.1 times 4.5.
Let's determine this product.
Before multiplying,
notice how 5.1 has one decimal place
and so does 4.5,
which means your product must contain two decimal places.
To begin, we multiply like we normally do.
So we first multiply by five, five times one is five,
five times five is 25.
Before multiplying by the four,
we add a zero to the rightmost place value,
and now multiplying by four, four times one is four
and four times five is 20.
And now we add,
but we know that your product
must contain two decimal places,
so starting on the right,
we move the decimal point over two places.
One, two,
the product is 22.95,
which means x equals 22.95
is the solution to the equation.
This means if we substitute 22.95 for x
back into the original equation,
it will satisfy the equation
or make the equation true.
And let's go ahead and check this.
Substituting 22.95 for x gives us 22.95
divided by 5.1 equals 4.5.
Now let's check the quotient.
Notice 22.95 divided by 5.1 is 4.5.
So the left side of the equation
is equal to the right side of the equation,
which verifies our solution is correct.
For the second example, we have 4.7 x equals 12.96,
so again, our goal is to determine the value of x
that satisfies the equation or makes the equation true
by isolating x on one side of the equation.
4.7 x means 4.7 times x.
To undo the multiplication and solve for x,
we need to divide both sides of the equation by 4.7.
On the left side of the equation,
4.7 divided by 4.7 simplifies to one,
leaving us one times x, which is x,
and now on the right, we need to find this quotient.
Let's go ahead and do this below.
We begin by making the divisor a whole number
by moving the decimal point one place to the right.
And now we do the same in the dividend.
And now we move the decimal point up into the quotient
and divide like we normally do.
We begin by determining how many 47s in 126, which is two.
Now I multiply two and the divisor,
two times 47 is 94.
Now we subtract, six minus four is two,
12 minus nine is three.
Bring down the nine,
and now determine how many 47s in 329.
Let's try seven.
Seven times seven is 49, record the nine,
perform an exchange with the four.
Seven times four is 28 plus four is 32.
Subtracting, notice how there are exactly seven 47s in 329
because this difference is zero,
and therefore, the quotient is 2.7.
X equals 2.7 is the solution to the equation.
Once again, this means if we substitute 2.7 for x
back into the original equation,
it will satisfy the equation
or make the equation true.
And let's go ahead and check this.
Performing this substitution gives us 4.7 times 2.7
equals 12.69,
and now we determine the product on the left.
And notice 4.7 times 2.7 is 12.69.
12.69 equals 12.69 is true,
verifying our solution as correct.
I hope you found this helpful.