Final answer:
When solving equations with variables on both sides, 'All Solutions' means that there are multiple values of the variable that satisfy the equation. It indicates that there is more than one possible solution.
Step-by-step explanation:
When solving equations with variables on both sides, 'All Solutions' means that there are multiple values of the variable that satisfy the equation and make it true. It indicates that there is more than one possible solution.
For example, let's consider the equation 2x + 3 = 5x - 1. To find all the solutions, we need to simplify and isolate the variable on one side. Here's how you can solve it:
- Start by subtracting 2x from both sides: 3 = 3x - 1.
- Add 1 to both sides: 4 = 3x.
- Divide both sides by 3: x = 4/3.
The solution to this equation is x = 4/3. However, it's important to note that there can be other values of x that satisfy this equation, resulting in multiple solutions.