Answer:
When solving an equation, if you arrive at a statement that is false or contradictory, it means that the equation has no solution. Here's how you can identify and solve an equation with no solution:
Explanation:
1. Start by simplifying the equation as much as possible by combining like terms and applying any applicable algebraic operations.
2. Follow the standard steps for solving equations, such as isolating the variable on one side of the equation.
3. If you reach a point where the equation simplifies to a false statement, such as "2 = 3" or "0 = 1," then you can conclude that the equation has no solution.
For example, let's consider the equation 2x + 5 = 2x + 10. Here's how we would approach solving it:
1. Start by simplifying both sides of the equation:
2x + 5 = 2x + 10
2. Subtract 2x from both sides to isolate the variable:
2x - 2x + 5 = 2x - 2x + 10
5 = 10
3. Since the simplified equation is false (5 is not equal to 10), we can conclude that the original equation has no solution.
In summary, an equation with no solution arises when the equation simplifies to a false statement, indicating that there is no value of the variable that satisfies the equation.