Question

decide whether the given equation has one solution, no solution, or infinitely many solutions.

$x - 13 = x + 1$

one solution no solution infinitely many solutions

explain your thinking.

Explanation:

Step1: Isolate x terms

Subtract $x$ from both sides:
$x - 13 - x = x + 1 - x$

Step2: Simplify both sides

Simplify to check consistency:
$-13 = 1$

of thinking:
When we subtract $x$ from both sides of the equation $x - 13 = x + 1$, we are left with $-13 = 1$, which is a false statement. This means there is no value of $x$ that can make the original equation true, so the equation has no solution.

Answer:

No solution