Write an equation with a variable on both sides of the equal sign that has no solution. Solve the equation and explain why it has no solution.
2x + 3 = 4x - 5
To solve for x, we need to isolate x on one side of the equation. Let's start by getting all the x terms on one side:
2x - 4x = -5 - 3
-2x = -8
Now, divide both sides by -2 to solve for x:
x = 4
Even though we found a solution for x, this equation actually has no solution. This is because when we substitute x = 4 back into the original equation, it does not hold true:
2(4) + 3 = 4(4) - 5
8 + 3 = 16 - 5
11 = 11
This is a true statement, which means that x = 4 is not the solution to the equation. In fact, there is no value of x that makes both sides of the equation equal, which is why this equation has no solution.