How many solutions does this equation have? 6 + p = p + 6

Answer 1

If you subtract p from each side you would get:

6 = 6.

Because this is always true, it does not matted what the value of p is! For example, if we go back to the original expression, you could plug in x = 2. Then you would have:

6 + 2 = 2 + 8

8 = 8, which is true.

This will work for any value of p (try a few values and convince yourself of this!)

Therefore, there will be infinite solutions to this equation because this is true for all values of p!

To check your understanding, think about the equation 5 + p = p + 6. How many solutions would this have?

Well, again, we can get rid of the p on both sides. Then we are left with:

5 = 6.

Is this true?

This is an incorrect statement so this equation would have no solution. No matter what value p is, 5 will never be equal to 6!

Hope this helped!