Answer :
- Add $\frac{1}{2}x$ to both sides of the equation $\frac{1}{2}x = -\frac{1}{2}x$.
- Simplify the equation to find $x = 0$.
- Verify the solution by substituting $x=0$ into the original equation.
- The value of $x$ is $\boxed{0}$.
### 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. Verifying the Solution
To verify the solution, we substitute $x=0$ back into the equation $\frac{1}{2}x = -\frac{1}{2}x$:$$\frac{1}{2}(0) = -\frac{1}{2}(0)$$ $$0 = 0$$Since the equation holds true, our solution is correct.
4. Final Answer
Therefore, the value of $x$ that satisfies the equation is 0.
### Examples
Understanding how to solve simple algebraic equations like this is crucial in many real-world scenarios. For instance, imagine you're balancing a budget where expenses need to equal income. If you find that half of your income is exactly offset by a debt, this problem demonstrates how to determine that your income and debt are both zero, indicating a balanced budget with no surplus or deficit. This kind of problem-solving is also applicable in physics, engineering, and computer science.
- Simplify the equation to find $x = 0$.
- Verify the solution by substituting $x=0$ into the original equation.
- The value of $x$ is $\boxed{0}$.
### 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. Verifying the Solution
To verify the solution, we substitute $x=0$ back into the equation $\frac{1}{2}x = -\frac{1}{2}x$:$$\frac{1}{2}(0) = -\frac{1}{2}(0)$$ $$0 = 0$$Since the equation holds true, our solution is correct.
4. Final Answer
Therefore, the value of $x$ that satisfies the equation is 0.
### Examples
Understanding how to solve simple algebraic equations like this is crucial in many real-world scenarios. For instance, imagine you're balancing a budget where expenses need to equal income. If you find that half of your income is exactly offset by a debt, this problem demonstrates how to determine that your income and debt are both zero, indicating a balanced budget with no surplus or deficit. This kind of problem-solving is also applicable in physics, engineering, and computer science.
