solve the equation if it an identity(all real numbers) or a contradiction(no solution) so state
5x+6+6x=10x+6+y
To determine whether the given equation is an identity (meaning it holds true for all real numbers) or a contradiction (meaning it has no solution), we can simplify the equation and compare the coefficients of the variables.
Let's start by simplifying the equation step by step:
5x + 6 + 6x = 10x + 6 + y
Combine the like terms on both sides:
11x + 6 = 10x + 6 + y
Now, let's isolate the variable "y" by transferring all other terms to the left side:
11x + 6 - 10x - 6 = y
Simplify further:
x = y
We have simplified the equation to x = y.
Since there are no numerical coefficients or constants involved, the equation x = y is an identity for all real numbers. This means that any value of "x" will equal the corresponding value of "y" for any given real number.
Therefore, the given equation is an identity for all real numbers.
subtract 10 x from each side.
x+6=y+6
x=y