Final answer:
To determine if an equation has one solution, no solutions, or infinite solutions, we need to solve the equation and analyze the result. If the equation simplifies to a true statement, then it has infinite solutions. If the equation simplifies to a false statement, then it has no solutions. And if the equation simplifies to a single value, then it has one solution.
Step-by-step explanation:
To determine if an equation has one solution, no solutions, or infinite solutions, we need to solve the equation and analyze the result. If the equation simplifies to a true statement, then it has infinite solutions. If the equation simplifies to a false statement, then it has no solutions. And if the equation simplifies to a single value, then it has one solution.
To find the value of the variable that makes the equation true, we can solve the equation by performing algebraic operations. For example, if the equation is 2x + 3 = 9, we can subtract 3 from both sides to isolate the variable. This gives us 2x = 6. Dividing both sides by 2, we find x = 3. Therefore, the equation has one solution, and the value of x that makes it true is 3.