Now, we'll take a look at solving two-step linear equations.
And, in order to isolate the variable, we'll first undo the addition or subtraction,
and then, undo the multiplication or division.
So, looking at the first example, we have four X plus seven equals negative 21.
So, in order to isolate the variable, we want to manipulate this equation so it is
in the form of X equals some number.
So, notice how we have four times X plus seven equals negative 21.
So, we'll first undo the addition, so the opposite of plus seven, will be minus seven.
So, we'll subtract seven on both sides of the equation.
So, plus seven minus seven would be zero.
So we'd have four X equals negative 21 minus seven, would be negative 28.
Again, we can think of this as negative 21 plus negative seven, if that helps.
And, now we have four times X equals negative 28, and four X means four times X. So,
to undo this multiplication we'll divide both sides by positive four.
Four divided by four is equal to one, and one times X is equal to X. And, negative 28 divided
by positive four is equal to negative seven.
So, our solution is X equals negative seven [writing on board].
Looking at the second example, we have negative two X minus nine equal's negative 21.
So again, to isolate the variable X, we want to manipulate the equation so that it's
in the form of X equals some number.
So, the first step would be to undo the subtraction, so we'll add nine to both sides
of the equation-- minus nine plus nine would simplify to zero.
So, we have negative two X equals negative 21 plus nine, is equal to negative 12.
And now, we have negative two times X equals negative 12.
So, we'll undo this multiplication by dividing both sides by negative two [writing on board].
Negative two divided by negative two is equal to one.
So, we have one X, or X equals negative 12 divided
by negative two is equal to positive six.
So, our solution is X equals six.
Let's take a look at two more examples.
Here we have X divided by three plus five equals negative four.
So again, we'll start by undoing the addition here.
So, we'll subtract five on both sides [writing on board].
So, plus five, minus five is zero.
So, we have X divided by three, equals negative four minus five.
Or we can think of this as negative four plus negative five, which would be negative nine.
And now we need to undo this division, with the opposite of dividing
by three, would be to multiply by three.
So we multiply the left side by three, we have to do the same to the right side.
And then here, dividing by three and multiplying by three into each other.
So, this simplifies to one X or X, and here we have negative nine times positive three
which is negative 27.
So, the solution is X equals negative 27.
And for the last example, I think it's going to be helpful
to write this first term as X divided by negative two.
Remember it doesn't matter whether this negative is in the front, in a numerator
or the denominator, but in this case, it's going to be easier to solve this if it's
in the denominator [writing on board].
So, we'll first undo the subtraction.
So, we'll add nine to both sides of the equation.
[ Writing on Board ]
Minus nine plus nine would be zero.
And negative two plus nine is equal to positive seven.
And now, we'll isolate the variable, by undoing this division
by multiplying both sides by negative two.
This multiplication division undo each other, so we're left with X. And on the right side,
we have positive seven, times negative two, which is equal to negative 14.
So, our solution is, X equals negative 14.