We want to solve the equation
three x plus three minus four equals
negative two x minus eight.
The solution to the equation is the value of x
that makes the expression three x plus three minus four
equal to negative two x minus eight.
In order to solve the equation for x,
we need to isolate x on one side of the equation.
But before we begin solving, we should check to see
if we can simplify either side of the equation.
Looking at the left side of the equation,
notice how we have two like terms here.
Because three minus four is equal to negative one,
the left side simplifies to three x plus negative one
or just three x minus one.
So now we have the equation three x minus one
equals negative two x minus eight.
Remember our goal here is to isolate x
on one side of the equation
and we cannot do this if we have an x term
on the left and an x term on the right,
and therefore the next step is
to get the x terms on one side.
We can do this by either undoing or eliminating
negative two x from the right
or undoing or eliminating three x from the left.
Let's undo the negative two x and we can do this
by adding two x to both sides of the equation.
Notice how negative two x plus two x equals zero.
Remember whatever operation we perform
to one side of the equation we must also perform
to the other to maintain equality.
And now simplifying both sides,
three x plus two x is five x
so we have five x minus one equals,
again negative two x plus two x is zero,
so the right side is now just negative eight.
The next step is to isolate the variable term
by adding or subtracting.
To isolate five x, we need to undo minus one
by performing the opposite or inverse operation.
And therefore to undo minus one,
the next step is to add one to both sides of the equation.
Simplifying again, again adding one undoes minus one
or negative one plus one is zero,
so now we have five x on the left equal
then the right negative eight plus one is negative seven.
Our last step is to solve for x by multiplying or dividing.
Five x means fives times x,
and therefore to undo multiplying by five,
we need to divide both sides by five.
Dividing by five undoes multiplying by five
and therefore this simplifies to just x
or five divided by five equals one,
one times x is x.
On the right side we have negative seven divided by five,
or negative 7/5,
and because the fraction does not simplify,
our solution is x equals negative 7/5.
Before we go though, let's verify our solution by replacing
negative 7/5 for x in the original equation to make sure
the left side of the equation equals the right side.
So performing the substitution,
we would have three times negative 7/5
plus three minus four equals
negative two times negative 7/5 minus eight.
Let's evaluate each side of the equation
using the calculator.
From the left we have three times negative 7/5
plus three minus four.
Enter.
Which is negative 5.2
or to get the fraction we press Math Enter Enter
which gives us negative 26/5.
On the right side we have negative two times
negative 7/5 minus eight.
Enter.
Which is also negative 5.2 or negative 26/5.
Which verifies our solution is correct.
The left side of the equation is equal to negative 26/5
when x equals negative 7/5 and so is the right.
This is our check to verify
we solved the equation correctly.
I hope you found this helpful.