In this context, you can think of the constants a, b and c being any number, including fractions, decimals, and negative numbers (but a cannot be the number 0).

The following are all examples of first-degree equations:

Even though some of the equations above don’t immediately look to be of the form of a first-degree equation, they can be manipulated to resemble the appropriate form.

I’m going to summarize the various steps you might need to take in order to solve a first-degree equation. The written steps will be the same steps we took in the video, but might work better for you to follow along with. I’ll explain the steps with the following equation:

1. Distribute any coefficients:

The -5 outside of the first set of brackets means that both the x and the 7 inside the brackets are being multiplied by -5, which gives us -5x - 35.

(We get -35 because -5x7 = -35)

The -2 outside of the second set of brackets means that both the 3 and the -x inside the brackets are being multiplied by -2, which gives us -6 + 2x.

(We get -6 because -2x3 = -6)

After doing this distributing we are left with the following:

2. Collect like terms:

We will now collect like terms. We cannot combine -5x and -35, for example, because they are not like terms. We can, however, combine -5x and 2x. When we do that, we are left with -3x (because -5 + 2 = -3). We can also combine -35 and -6, to get -41.

After collecting like terms we have:

3. Undo operations with the goal of isolating x on its own:

To solve equations, we employ backwards BEDMAS which means we undo addition and subtraction before we undo multiplication and division.

To undo the subtraction of -41 on the left side of our equation, we add +41 to the same side. When we do this, we get rid of the -41 because -41 + 41 = 0.

But we can’t just add 41 to the left side. Because we are dealing with an equation, whatever we do to one side, we have to do to the other so we don’t change the equation. Therefore, because we added 41 to the left side to get rid of the -41, we will also add 41 to the right side.

Then we are left with:

Now, we want to undo the multiplication by -3 on x, to get x by itself. To undo this multiplication by -3, we divide by -3. Because -3/3 = 1, we are just left with 1x or x on the left side.

But again, whatever we do to one side, we must do to the other. Therefore, we divide 47 by -3. This gives us the following: