In this video,
we will solve a linear equation in one variable
with variable terms on both sides of the equation.
We're asked to solve the equation two m minus nine
equals six m
minus 17.
We should first notice the equation
does not contain any fractions or decimals
that can be cleared from the equation.
And also, neither side of the equation simplifies,
which means the first step is to add or subtract
in order to isolate the variable term
on one side of the equation.
Well, notice right now we have a variable term
on the left and on the right,
which means the first step is to decide
whether we want to isolate the variable term
on the left or right.
In this video, we will show both methods,
but to begin, let's isolate the variable term
on the right side of the equation,
which means on the left side of the equation,
we need to add or subtract to undo positive two m.
And therefore, the first step is to subtract two m
on both sides of the equation.
On the left, two m minus two m is zero,
which is why we subtracted two m on both sides.
We now just have negative nine on the left side.
Negative nine equals
on the right six m minus two m is four m.
The right side is now just four m minus 17.
We still have not isolated the variable term though.
We need to undo this subtraction
in order to isolate the variable term for m.
To undo minus 17, we need to add 17
to both sides of the equation.
On the left, negative nine plus 17 is positive eight.
We have eight equals
on the right negative 17 plus 17 is zero.
The right side is now just four m.
Now that we've isolated the variable term,
the last step is to multiply or divide
to solve the equation for m.
Because four m means four times m,
to undo the multiplication and solve for m,
we now divide both sides by four.
Simplifying, eight divided by four is equal to two.
On the right side, four divided by four is equal to one.
One times m is m.
Two equals m is equivalent to m equals two,
which is the solution to the equation.
Notice how by isolating the variable term
on the right side of the equation,
the m term had a positive coefficient.
Now let's solve this equation again
and isolate the variable term on the left side
to compare the two possible methods.
After we do this, we will verify the solution.
So beginning with the given equation again,
let's now isolate the variable term
on the left side of the equation, which means now we go over
to the right side of the equation.
And we need to add or subtract to undo positive six m,
which means now the first step will be to subtract six m
on both sides of the equation.
On the left, two m minus six m is negative four m.
The left side is now negative four m minus nine equals
on the right side six m minus six m is zero.
Right side is now just negative 17.
Looking at the left side of the equation,
we still need to add or subtract
to isolate the variable term negative four m,
which means we need to undo minus nine
by adding nine to both sides of the equation.
On the left side, we have negative four m,
and then negative nine plus nine is zero.
We have negative four m equals
negative 17 plus nine equals negative eight.
Now that we've isolated the variable term,
the last step is to multiply or divide
to solve the equation for m.
Because negative four m means negative four times m,
to undo the multiplication and solve for m,
we divide both sides by negative four.
Simplifying, negative four divided by negative four is one.
One times m is m.
We have m equals
negative eight divided by negative four is positive two,
giving us the same solution, which we should expect.
But notice how by isolating the variable term
on the left side of the equation this time,
the m term had a negative coefficient.
But again, either method does work.
Now let's go ahead and verify our solution by verifying
if we substitute two for m in the original equation,
it does satisfy the equation.
Beginning with the given equation,
we will now substitute two for m
here and here
and verify the left side of the equation
is equal to the right side.
From this substitution, we have two times two minus nine
equals six times two minus 17.
Simplifying both sides of the equation,
we multiply before subtracting.
Two times two is four.
On the left, we have four minus nine
equals on the right 12 minus 17.
Four minus nine is equal to negative five,
and 12 minus 17 is also equal to negative five.
Negative five equals negative five is true,
verifying the solution is correct.
I hope you found this helpful.