An equation that has only one solution is generally referred to as a linear equation. A common form of a linear equation is ax + b = c, where a, b, and c are constants and a is not equal to zero. When we solve for x, we find a unique value that satisfies the equation.
For example, consider the equation 2x + 4 = 10. To find the solution, we can follow these steps:
- Subtract 4 from both sides: 2x = 10 – 4 → 2x = 6
- Divide both sides by 2: x = 6 / 2 → x = 3
In this case, the only solution is x = 3. In contrast, equations like x^2 = 4 or (x – 2)(x + 2) = 0 can have two solutions, demonstrating that not all equations are created equal in terms of the number of solutions.
To summarize, a linear equation of the form ax + b = c will always yield a single solution provided that a is not zero, making it a straightforward example of an equation with one solution.