show all of your work when solving the equation 5x-6 = -4 + 5x. How many solutions does the equation have? How could you have determined this by first examining both sides of the equation to begin with?

Question

-7 pts for showing your work
-1 pt for identifying amount of solutions
-2 pts for explaining how you could determine amount of solutions by examining equation to begin with

Answer 1

To solve the equation 5x - 6 = -4 + 5x, we can start by simplifying both sides.

5x - 6 = -4 + 5x

Now, we can move all the variables (5x) to one side of the equation and all the constants (-6 and -4) to the other side.

5x - 5x = -4 + 6

0 = 2

Since 0 does not equal 2, this equation is inconsistent and has no solutions.

Therefore, the equation has 0 solutions.

To determine the number of solutions by examining the sides of the equation, we can see that when all variables are moved to one side, the equation simplifies to a false statement (0 = 2). This indicates that the equation is inconsistent and has no solutions. Therefore, by examining the equation and seeing that it simplifies to a false statement, we can determine that the equation has 0 solutions.