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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 $x = 0$.
- The solution to the equation is $\boxed{0}$.
### Explanation
1. Understanding the Equation
We are given the equation $\frac{1}{2}x = -\frac{1}{2}x$ and asked to find the value of $x$ that satisfies it. This is a linear equation, and we can solve it by isolating $x$ on one side of the equation.
2. Solving for x
To solve the equation $\frac{1}{2}x = -\frac{1}{2}x$, we can add $\frac{1}{2}x$ to both sides of the equation. This gives us
$$\frac{1}{2}x + \frac{1}{2}x = -\frac{1}{2}x + \frac{1}{2}x$$
$$\frac{1}{2}x + \frac{1}{2}x = 0$$
Since $\frac{1}{2} + \frac{1}{2} = 1$, we have
$$1x = 0$$
$$x = 0$$
3. Final Answer
Therefore, the value of $x$ that satisfies the equation $\frac{1}{2}x = -\frac{1}{2}x$ is $x = 0$.
### Examples
This type of equation can appear when modeling situations where rates of change are equal and opposite. For example, imagine two objects moving towards each other at the same speed. If you set up an equation to track their relative positions, you might encounter a similar equation where the variable represents time. Solving it helps you determine when they meet.
- Simplify the equation to $x = 0$.
- The solution to the equation is $\boxed{0}$.
### Explanation
1. Understanding the Equation
We are given the equation $\frac{1}{2}x = -\frac{1}{2}x$ and asked to find the value of $x$ that satisfies it. This is a linear equation, and we can solve it by isolating $x$ on one side of the equation.
2. Solving for x
To solve the equation $\frac{1}{2}x = -\frac{1}{2}x$, we can add $\frac{1}{2}x$ to both sides of the equation. This gives us
$$\frac{1}{2}x + \frac{1}{2}x = -\frac{1}{2}x + \frac{1}{2}x$$
$$\frac{1}{2}x + \frac{1}{2}x = 0$$
Since $\frac{1}{2} + \frac{1}{2} = 1$, we have
$$1x = 0$$
$$x = 0$$
3. Final Answer
Therefore, the value of $x$ that satisfies the equation $\frac{1}{2}x = -\frac{1}{2}x$ is $x = 0$.
### Examples
This type of equation can appear when modeling situations where rates of change are equal and opposite. For example, imagine two objects moving towards each other at the same speed. If you set up an equation to track their relative positions, you might encounter a similar equation where the variable represents time. Solving it helps you determine when they meet.
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