Problem 38 Solve equation, and check your s... [FREE SOLUTION]

Chapter 2: Problem 38

Solve equation, and check your solution. \(-x=-\frac{1}{2}\)

Short Answer

Expert verified

x = \frac{1}{2}\

Step by step solution

Isolate the Variable

To solve \(-x = -\frac{1}{2}\), we need to isolate the variable \(x\). In this case, we can simply multiply both sides by \(-1\) to get \(x\) by itself.

Simplify the Equation

Multiplying both sides by \(-1\), we have: \(-1 \cdot -x = -1 \cdot -\frac{1}{2}\). This simplifies to \(x = \frac{1}{2}\).

Check the Solution

Substitute \frac{1}{2}\ for \(x\) in the original equation \(-x = -\frac{1}{2}\) to verify the solution: \-\frac{1}{2} = -\frac{1}{2}\. Since both sides of the equation are equal, the solution \(x = \frac{1}{2}\) is correct.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Isolate the Variable

The first step in solving a linear equation like \-x = -\frac{1}{2} is to isolate the variable. This means we need to manipulate the equation so that the variable, in this case \(x\), stands alone on one side of the equation. Since there is a negative sign attached to \(x\), we need to get rid of it. To do this, multiply both sides of the equation by \(-1\).
This will reverse the sign of both sides giving us:
\(-1 \cdot -x = -1 \cdot -\frac{1}{2}\).
Now, the equation simplifies and we're left with \(x\) isolated.
So, multiplying both sides, we get: \(x = \frac{1}{2}\).

Simplify the Equation

After isolating the variable, the next step is to simplify the equation. We've already multiplied both sides by \(-1\) in the previous step:
\(-1 \cdot -x = -1 \cdot -\frac{1}{2}\).
When we do the multiplication:
\-1 \cdot -x\ becomes \(x\),
and \-1 \cdot -\frac{1}{2}\ becomes \(\frac{1}{2}\).
So, the equation simplifies to:
\(x = \frac{1}{2}\).
Now we've found our solution to the equation. It's always good practice to simplify equations as much as possible to avoid mistakes.

Check the Solution

The final step in solving any equation is to check your solution. This ensures that the solution is correct. To check the solution of the equation \-x = -\frac{1}{2}\, we substitute the value we found for \(x\).
Substitute \(\frac{1}{2}\) for \(x\) in the original equation:
\-\frac{1}{2} = -\frac{1}{2}\.
Since both sides of the equation are equal, the solution is verified as correct.
Hence, the solution \(x = \frac{1}{2}\) is indeed correct.
This final step is crucial, as it confirms that all our steps have been performed correctly and the right answer has been reached.

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91影视

Solve equation, and check your solution. \(-x=-\frac{1}{2}\)

Short Answer

Step by step solution

Isolate the Variable

Simplify the Equation

Check the Solution

Key Concepts

Isolate the Variable

Simplify the Equation

Check the Solution

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