First Response

Eric,

When you are asked to solve the equation 3x + 5 = 11 you are looking for all numbers x that make the left side equal to the right side. In this case you find one number, x = 2. Thus the solution set contains one number, 2.

When you are asked to solve x² + x - 6 = 0 you are again looking for all numbers x that make the left side equal to the right side. In this case there are two values for x, x = 2 and x = -3. Thus the solution set contains the two numbers 2 and -3.

When you are asked to solve x² + 2x = x(x + 2) you are again looking for all numbers x that make the left side equal to the right side. Expanding the right side results in the equation x² + 2x = x² + 2x. In this case substitution of any number x results in the left side and the right side being equal. Thus the solution set is all real numbers.

I hope this helps,
Penny

Second Response

Hi Eric. That equation is actually meaningless!

If you multiply out the right hand side of the equation, you get the same thing as the left hand side, so everything cancels and you are left with the truism 0 = 0. This means that the equation doesn't actually depend on x at all, so x can have any value you want! Try it.

Stephen La Rocque.