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Answer :
- Add $\frac{1}{2}x$ to both sides of the equation $\frac{1}{2}x = -\frac{1}{2}x$.
- Simplify the equation to get $x = 0$.
- The value of $x$ that satisfies the equation is 0.
- Final Answer: $\boxed{0}$
### Explanation
1. Understanding the Equation
We are given the equation $\frac{1}{2}x = -\frac{1}{2}x$. Our goal is to find the value of $x$ that satisfies this equation.
2. Solving for x
To solve for $x$, we can add $\frac{1}{2}x$ to both sides of the equation:$$\frac{1}{2}x + \frac{1}{2}x = -\frac{1}{2}x + \frac{1}{2}x$$This simplifies to:$$x = 0$$
3. Final Answer
Therefore, the value of $x$ that satisfies the equation $\frac{1}{2}x = -\frac{1}{2}x$ is 0.
### Examples
This problem demonstrates how to solve a simple algebraic equation. In real life, such equations can model various situations, such as balancing costs and revenues in a business, calculating the required amount of ingredients in a recipe, or determining the equilibrium point in a physical system. Understanding how to solve these equations is fundamental to making informed decisions and solving practical problems.
- Simplify the equation to get $x = 0$.
- The value of $x$ that satisfies the equation is 0.
- Final Answer: $\boxed{0}$
### Explanation
1. Understanding the Equation
We are given the equation $\frac{1}{2}x = -\frac{1}{2}x$. Our goal is to find the value of $x$ that satisfies this equation.
2. Solving for x
To solve for $x$, we can add $\frac{1}{2}x$ to both sides of the equation:$$\frac{1}{2}x + \frac{1}{2}x = -\frac{1}{2}x + \frac{1}{2}x$$This simplifies to:$$x = 0$$
3. Final Answer
Therefore, the value of $x$ that satisfies the equation $\frac{1}{2}x = -\frac{1}{2}x$ is 0.
### Examples
This problem demonstrates how to solve a simple algebraic equation. In real life, such equations can model various situations, such as balancing costs and revenues in a business, calculating the required amount of ingredients in a recipe, or determining the equilibrium point in a physical system. Understanding how to solve these equations is fundamental to making informed decisions and solving practical problems.
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