Rewrite the equation to find X: y = 3x + 5

Answer 1

This equation shows us what y is equal to, but now we need to rearrange it to find x. Let's work through this process.

First, we take our original equation and move everything that is not connected to x (through multiplication or division) to the other side. In this case, we have the + 5 that is separate from the x. To get rid of this 5, we have to subtract 5 from both sides of the equation (so that we keep both sides equal to one another; if we subtract 5 from only one side, that would make the 3x + 5 side unequal to the y side).

y – 5 = 3x + 5 – 5

So we get:

y – 5 = 3x

Now we need to get rid of that 3 from the 3x, so we can have x all by itself. To do this, we need to divide both sides by 3:

(y – 5) / 3 = 3x / 3

So we get:

(y – 5) / 3 = x

or

x = (y – 5) / 3

To review the steps for a problem like this:

1. Identify what you're looking to solve. In this case, we knew we wanted to solve for x.
2. Reorganize the equation by first bringing everything added or subtracted that isn't what you want to the other side of the equation. In this case, we subtracted 5 from both sides of the equation to isolate the 3x on the x side.
3. Keep reorganizing the equation by getting rid of everything that is multiplied or divided to what you want. In this case, we divided 3 from both sides of the equation to isolate the x.
4. By this point, you should have isolated what you want on one side of the equation. It gets slightly more complicated if you introduce other things to the equation, like parentheses or exponents, but these steps should take care of this basic form of an equation.

As a bonus, I'll walk you through one more example, this time with a starting equation that has division and subtraction. Again, we'll solve for x.

Example:

y = x/2 – 7

Add 7 to both sides to isolate x/2:

y + 7 = x/2 – 7 + 7

y + 7 = x/2

Now we'll have to multiply both sides by 2 to isolate x:

(y + 7) * 2 = x/2 * 2

2(y + 7) = x

We can multiply the 2 through the y + 7 if we want to simplify things:

2y + 14 = x

And I like to have the x shown on the left side, so we can more easily see what we were looking for:

x = 2y + 14

With this framework, you should be able to solve all problems like this.