91Ó°ÊÓ

In solving linear equations, one of the core steps is to isolate the variable. This means manipulating the equation so that the variable (e.g., \(x\)) is on one side of the equation by itself.
Often, this involves applying inverse operations, like addition, subtraction, multiplication, or division.
In our example, the given equation is \( \frac{1}{4}x = -12 \).
Since the variable \(x\) is being multiplied by \( \frac{1}{4} \), we can isolate \(x\) by doing the opposite—multiplying both sides of the equation by 4.
This step effectively cancels out the \( \frac{1}{4} \), leaving us with: \( x = -12 \times 4 \).
It's crucial to perform the same operation on both sides of the equation to keep it balanced.

The next step in solving the equation \( \frac{1}{4}x = -12 \) is to perform the multiplication.
After isolating the variable, we reached \( x = -12 \times 4 \).
To find the value of \(x\), we simply multiply \(-12\) by \(4\).
Here's the multiplication:
-12 times 4 equals -48.
Therefore, \(x = -48\). Multiplying numbers, especially when dealing with negative values, might require extra attention:
- Two negative numbers multiplied together give a positive result.
- A positive number with a negative number results in a negative value.
Hence, \( -12 \times 4 = -48 \).

Verifying the solution is a critical step to ensure the accuracy of your work.
To verify, substitute the solution back into the original equation and check if both sides are equal.
We found \(x = -48\)
Plugging this back into the equation, we get: \(\frac{1}{4} (-48) = -12 \).
Now, simplify the left side:
\(\frac{1}{4} (-48) = -12 \).
Since \(-12 = -12 \) holds true, we confirm that our solution \(x = -48\) is indeed correct.
Always remember this step because it helps to catch any potential errors made during the process.
By verifying, you build confidence that you have correctly solved the equation.