Question

does the equation x = x + 3 have one solution, no solutions, or infinitely many solutions?
first, lets try to isolate the variable, x, to get x by itself on one side of the equation. there are x terms on both sides of the equation. one way you could solve is to get rid of the x term from one of the sides. what move can you make to get rid of the x term on the right side of the equation while keeping the equation balanced?
x = x + 3
subtract x from each side
add x to each side
multiply each side by x

Explanation:

Step1: Choose valid operation to isolate $x$

To eliminate $x$ from the right side while keeping the equation balanced, we subtract $x$ from each side.

Step2: Perform the operation

$$x - x = x + 3 - x$$
$$0 = 3$$
This is a false statement, meaning no value of $x$ can satisfy the original equation.

Answer:

1. The correct operation to balance the equation: Subtract $x$ from each side
2. The equation $x=x+3$ has no solutions.