Give an explanation on how many solutions this equation has? 4x + 22 = 8x + 10

Answer 1

To determine how many solutions the equation has, we'll solve for x by rearranging terms and simplifying. Starting with the equation:

4x + 22 = 8x + 10

First, we want to get all terms with an x on one side and the constant terms on the other. We can do this by subtracting 4x from both sides:

4x + 22 - 4x = 8x + 10 - 4x

Which simplifies to:

22 = 4x + 10

Next, we subtract 10 from both sides to isolate the term with x:

22 - 10 = 4x + 10 - 10

12 = 4x

Now we'll solve for x by dividing both sides by 4:

12 / 4 = 4x / 4

3 = x

So there is one unique solution to this equation:

x = 3

Therefore, the equation 4x + 22 = 8x + 10 has a single solution, x = 3.