Answer :
- Start with the equation $\frac{1}{2}x = -\frac{1}{2}x$.
- Add $\frac{1}{2}x$ to both sides, resulting in $x = 0$.
- The solution to the equation is $\boxed{0}$.
### Explanation
1. Analyzing the equation
Let's analyze the given equation and the steps taken by Marissa. The original equation is $-(x-14)+11=\frac{1}{2} x-(x-4)$. Marissa's work is shown as:
$\frac{1}{2}(x-14)+11=\frac{1}{2} x-(x-4)$
$\frac{1}{2} x-7+11=\frac{1}{2} x-x+4$
$\frac{1}{2} x+4=-\frac{1}{2} x+4$
When she subtracts 4 from both sides, $\frac{1}{2} x=-\frac{1}{2} x$ results. We need to find the value of $x$.
2. Solving for x
We are given the equation $\frac{1}{2}x = -\frac{1}{2}x$. To solve for $x$, we can add $\frac{1}{2}x$ to both sides of the equation:
$$\frac{1}{2}x + \frac{1}{2}x = -\frac{1}{2}x + \frac{1}{2}x$$
$$x = 0$$
3. Final Answer
Therefore, the value of $x$ that satisfies the equation $\frac{1}{2}x = -\frac{1}{2}x$ is $x = 0$.
### Examples
Understanding how to solve simple algebraic equations like this is fundamental in many areas of life. For example, if you're trying to balance a budget where your income and expenses need to be equal, you might use a similar equation to find out how much you need to save or cut back on spending to reach a balanced state. This kind of problem-solving is also crucial in fields like engineering, economics, and computer science.
- Add $\frac{1}{2}x$ to both sides, resulting in $x = 0$.
- The solution to the equation is $\boxed{0}$.
### Explanation
1. Analyzing the equation
Let's analyze the given equation and the steps taken by Marissa. The original equation is $-(x-14)+11=\frac{1}{2} x-(x-4)$. Marissa's work is shown as:
$\frac{1}{2}(x-14)+11=\frac{1}{2} x-(x-4)$
$\frac{1}{2} x-7+11=\frac{1}{2} x-x+4$
$\frac{1}{2} x+4=-\frac{1}{2} x+4$
When she subtracts 4 from both sides, $\frac{1}{2} x=-\frac{1}{2} x$ results. We need to find the value of $x$.
2. Solving for x
We are given the equation $\frac{1}{2}x = -\frac{1}{2}x$. To solve for $x$, we can add $\frac{1}{2}x$ to both sides of the equation:
$$\frac{1}{2}x + \frac{1}{2}x = -\frac{1}{2}x + \frac{1}{2}x$$
$$x = 0$$
3. Final Answer
Therefore, the value of $x$ that satisfies the equation $\frac{1}{2}x = -\frac{1}{2}x$ is $x = 0$.
### Examples
Understanding how to solve simple algebraic equations like this is fundamental in many areas of life. For example, if you're trying to balance a budget where your income and expenses need to be equal, you might use a similar equation to find out how much you need to save or cut back on spending to reach a balanced state. This kind of problem-solving is also crucial in fields like engineering, economics, and computer science.
