Question 6600
When you end up with 1 = 1 at the end, or a number equals itself after going through algebraic manipulations, the solution is the set of all real numbers.


However, in this case, you have 2x-5 and 2x+5 in the denominators. Remember that the denominator can NEVER be zero. In this example, the values 5/2 and -5/2 will make the denominator zero. The solution then would be the set of real numbers except +-5/2.


Just in case it might look like I skipped steps, We'll have the equations 2x - 5 = 0 AND 2x + 5 = 0. We are NOT solving for x here. We are just setting the denominators to equal zero to find out what x values make the denominators zero. When you "solve for x" (that is, to find that troublemaker x value), you're finding the value or values that will make your equation NOT WORK FOR SURE.