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