Quandaries and Queries


Who is asking: Student
Level of the question: Secondary

Question: 14p - 8 = 22 + 20p



Hi Tiffany,

Sometimes I think of an equation as a balance with the balance point at the equal sign and weights on both sides that balance. The goal is to manipulate the weights on both sides so that the balance is not disturbed but you end with the variable (p in your example) alone on one side of the equation and a number on the other side.

In your example I would start by subtracting 14p from both sides of the equation. This will maintain the balance and result no p's on the left side.

14p - 8 = 22 + 20p
-14p + 14p - 8 = 22 + 20p - 14p
-8 = 22 + 6p

I now have p on only one side of the equation but I want to eliminate the 22 on the right side so I subtract 22 from both sides. Again, since I am subtracting 22 from both sides the balance will be maintained.

-8 = 22 + 6p
-22 - 8 = -22 + 22 + 6p
-30 = 6p

We're almost there. I want p alone on the right and I can accomplish this by dividing both sides by 6. This gives

-30 = 6p
-30/6 = 6p/6
-5 = p

Since we read from left to right your textbook and your teacher probably write this

p = -5