The solution to the equation
is the value of the variable that satisfies the equation,
or makes the equation true.
In order to solve the equation,
we need to isolate the variable on one side of the equation.
For the first step, we need to simplify
both sides of the equation.
For this equation, we can simplify the left side
of the equation by clearing the parentheses
and combining like terms.
To clear parentheses, we distribute eight.
Distributing eight, we have eight times x, which is eight x
minus eight times five, which gives us minus 40.
And then we still have minus four equals 28 x minus 204.
Notice the right side is not simplified because,
we don't have like terms.
But we do have like terms on the left,
we can combine the negative 40 and negative four.
Negative 40 minus four is equal to negative 44.
And therefore the left side simplifies
to eight x minus 44 equals 28 x minus 204.
And now for the next step, we need to add or subtract
to isolate the variable terms on one side of the equation.
That is right, now we have eight x on the left
and 28 x on the right.
So we can either undo the positive 28 x
by subtracting 28 x on both sides,
or we can undo the positive eight x
by subtracting eight x on both sides.
Normally, we prefer the variable on the left side,
so let's go ahead and subtract 28 x on both sides.
Simplifying on the left, eight x minus 28x is negative 20 x.
We still have minus 44 equals on the right side,
28 x minus 28 x is zero.
The right side simplifies to negative 204.
Still isolating the variable term,
we need to undo the minus 44 by adding 44
to both sides of the equation.
Simplifying, negative 44 plus 44 is zero.
The left side simplifies to negative 20 x,
equals on the right side, we have negative 204 plus 44.
Notice for this sum, the negative 204
is going to outweigh the positive 44.
And because we're adding images with different signs,
we have to subtract the absolute values,
to determine how much the negative 204 outweighs
the positive 44.
The absolute value of negative 204 is 204,
the absolute value 44 is 44 and now we subtract.
The difference here is 160.
But because the native 204 had the larger absolute value,
or because it outweighs the positive 44,
the sum is negative 160.
And now for last step, we multiply or divide
in order to solve for x.
And since negative 20 x means negative 20 times x,
to undo the multiplication and solve for x,
we divide both sides by negative 20.
Simplifying, negative 20 divided by itself,
simplifies the one, one times x is x.
We have x equals negative 160 divided by negative 20,
which is equal to positive eight.
The solution to the equation is x equals eight,
which means eight will satisfy the equation.
And let's go ahead and check this by substituting
eight for x back into the original equation.
Performing the substitution we have eight,
times the quantity eight minus five
and then minus four, which must be equal
28 times eight minus 204.
Let's evaluate both expressions using the calculator.
The expression on the left is equal to 20.
The expression on the right is also equal to 20.
And since 20 equals 20 is true,
this verifies our solution as correct.
I hope you found this helpful.