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4y + 15 = 6y - 45

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Hi Donovan. The goal in this problem is to get y on one side of the equal sign by itself. This is called isolating the variable. As you can see, y shows up on both sides in the problem. We will want to pick a side to move all the y terms to. It doesn't matter which side we choose.

4y + 15 = 6y - 45

Let's move all the y terms to the right side. We do this by adding or subtracting a term from both sides to get rid of all the y's on the left side of the equal sign. Notice that the y term on the left side is 4y. So lets subtract 4y from both sides.

4y + 15 - 4y = 6y - 45 - 4y

We can do this as long as we do the same thing to both sides of the equation.

Rearrange:

4y  - 4y + 15= 6y  - 4y - 45

Combine the y terms. On the left side, 4y - 4y becomes 0. On the right side, 6y - 4y is 2y.

15= 2y  - 45

The y terms are all on the right side of the equal sign. Now we want to move all the numeric terms to the left side. Start with things that are being added or subtracted to the y term. In this problem, we want to get rid of that -45 term on the right side of the equal sign. We do this by adding 45 to both sides:

15 + 45 = 2y - 45 + 45

60 = 2y

The only thing that remains is to move that 2 to the left side. Notice that we can't subtract or add anything to get rid of just the 2 because it is being multiplied by the y. To get rid of the 2, we divide both sides by 2.

60/2  = 2y/2

30 = y

That is our answer. y = 30. To check it, we rewrite the original equation and plug in 30 for each y. If this makes the equation true, then our answer is correct.

4y + 15 = 6y - 45

4(30) + 15 = 6(30) - 45

120 + 15 = 180 - 45

135 = 135 TRUE! Therefore our answer (y=30) is the correct solution to the equation.