19-8d=d-17 how do i solve this?

Question

How can i solve this equation?

Answer 1

Questions like these almost always warrant one step:

Isolate the variables (any term that has a letter associated with it; for example: x, d, m etc) from constants (plain numbers).

Keeping that in mind, put all the variables on the left hand side of the equation, and all the constants on the right hand side.

19-8d=d-17

∴ -8d - d = - 17 - 19 (when you take anything from the one side of the equation and put it on the another, the operation on that constant/variable changes as well. If it was 19 (positive 19) on one side, it becomes -19 on the other. This, of course, is the quick way of doing things. (For the mathematical explanation, refer to Roberto's answer).

∴ - 9d = - 36

Dividing by -9 on both sides, we would get

d = 4 (since -9 ÷ -9 = 1, and -36 ÷ 9 = 4)

Here's, really quickly, how to solve any other similar problems:

1. Isolalte the variables from the constants by bringing all variables to one side and all constants to another.
2. Perform the remaining operations, and you have your final answer!

Good luck solving other similar problems.

Answer 2

19-8d = d-17  

I advise my students to start with the unknown (d).  If you eliminate the smaller one, you will deal with positive values.  So, let's eliminate -8d; how? add 8d on both sides of the equal sign:

19-8d+(8d) = d-17+(8d)  

The parenthesis are not necessary, I use it as a mean of highlighting the operation.

Now, simplify:

19 = 9d-17    Now it is time to add 17 on both sides:

19 + (17) = 9d-17 + (17)

36 = 9d   Now, divide by 9 on both sides:

36 ÷ 9 = 9d ÷ 9

4 = d; or d = 4    

Finally, it is important that you check your answer, even if you're not being asked to do it.  Getting the habit of checking your answer is important, because sometimes we make silly mistakes that can be located and corrected easily, if we find that our answer is wrong.  OK, let's check the answer:

19-8d = d-17   since d=4, substitute:

19-8(4) = 4-17  ??? true, or false ???

19-32 = -13  Yes, this is a true statement.  Our answer is correct!!