One of the first types of linear equations that you will learn how to solve are called
one step linear equations.
Ah, these are a good introduction into how to solve linear equations uhm, they're not
the most difficult type of exercises but uh, they are very, very, popular.
So let's take a look at how we solve one step linear equations.
Ah, the reason they call them one step equations is they literally take one step to solve,
to get your answer to solve for x, or whatever your variable is.
And the step that you'll be taking is either using the addition property, or the multiplication
property.
And the reason, or way that you know which property to use, is you are going to be doing
the opposite of whatever is done to x.
And the mathematical word for this is the inverse operation.
So for example if x is being added by something, we're going to subtract.
Or if it's multiplied, we're going to divide.
We're always going to do the opposite of whatever is done to our variable.
And that's going to help us solve for X.
So let's look at few examples.
So here we go, first example, they want us to solve the equation, two x equals twelve.
When they say solve, what they mean is isolate the x, get the x by itself.
Well the x is being multiplied by two.
So I want to solve for x in one step.
And since x is multiplied by two, I'm going to divide by two.
And the reason that's a good idea is the times two, and divide by two negate each other,
and cancel each other.
And uh, then we would just have x by itself on the left-hand side.
But here's where the multiplication or addition properties are going to come in.
If you are going to multiply or divide the left side by a certain number, you need to
do the same thing to the right-hand side.
So since we divided the left side by two, we're also going to divide the right side
by two.
And twelve divided by two is six.
So six would be our final answer.
This would be the solution to this linear equation.
Now one other way to say this is instead of two x equals twelve, instead of dividing or
using that language, you could easily say multiply by a half, and that has the same
effect.
Multiplying by a half is like dividing by two.
Two times a half is one.
And so we get x equals twelve times a half, which is six.
Which is the same answer as what we have here.
Let's try another one.
Let's say we have the equation four equals negative seven, plus y.
I'd like to isolate the y, I'd like to solve for y.
Right now I have an extra negative seven on the right-hand side that I don't want.
This is like subtracting seven that, that I don't want on the right-hand side.
So the opposite of that would be to add seven to the right-hand side.
But remember the addition property, if you add seven to the right, to keep this equality
maintained right here.
You also have to add seven to the left, so that everything stays balanced.
Minus seven and plus seven, they cancel, and so we get eleven.
Four plus seven, eleven equals y, or obviously you could say y equals eleven.
The uh, order in which you write the signs doesn't matter.
So there's our solution to this equation.
And you can check your answer by replacing y with eleven.
Negative seven plus eleven is in fact four.
So that is the right answer.
Alright last example, ten m equals five.
Well we're going to look at what is being done to m, and we're going to do the opposite.
Well m is being multiplied by ten, so we are going to divide by ten.
And what's nice about that, the reason that works well, is that would make the tens cancel.
Times ten and divide by ten cancel each other.
You would just get an m, equal to five over ten.
And make sure we are dividing both sides by ten.
So five over ten, that's a fraction and which is okay, that's totally fine.
uh, and matter of fact, that fraction will reduce to one half.
So our solution would be m equals a half.
And just like before, we can go back and check our answer.
If we think one half is our solution for m.
Let's go back to the white equation, ten m equals five.
Ten times a half is five.
So that is in fact the correct solution.
So ah, just remember for these one step equations, uhm, basically you're just going to do the
opposite of whatever is done to x.
It should only take you one step to solve for your variable.