91Ó°ÊÓ

When solving linear equations, one of the primary goals is to **isolate the variable**. In our example, the variable is \( k \). Isolating the variable means we want \( k \) to be on one side of the equation by itself. This makes it possible to determine its value directly.
For instance, in the equation \( 92 = \frac{k}{2} \), \( k \) is currently being divided by 2. To isolate \( k \), we'll need to perform operations to both sides of the equation that get \( k \) alone on one side.
In linear equations, this typically involves doing the opposite of what is currently being done to the variable. Here, since \( k \) is being divided by 2, our next step will be to multiply by 2 to cancel out the division.

Fractions can make solving equations look complex. One of the first steps we take is to **remove fractions** so the equation becomes simpler.
In our exercise, we initially have the equation \( 92 = \frac{k}{2} \). The fraction here is \( \frac{k}{2} \).
To remove the fraction, we multiply both sides of the equation by the denominator of the fraction. In this case, the denominator is 2:

• Multiply both sides by 2: \( 92 \times 2 = \frac{k}{2} \times 2 \)

This cancels the 2 in the denominator on the right side, and we get:
\( 184 = k \). Now, we no longer have the fraction, and isolating the variable becomes much easier.

Taking **simplification steps** is crucial when solving linear equations. Simplification makes the equation more manageable and brings us closer to the solution in each step.
In our example, after removing the fraction by multiplying both sides by 2, we had: \( 92 \times 2 = k \).
Perform the multiplication on the left side:

• \( 92 \times 2 = 184 \)

So, we then have \( k = 184 \).
Simplifying each side of the equation involves:

• Performing any arithmetic operations like addition, subtraction, multiplication, or division.
• Ensuring logical steps are followed to maintain the equation's balance.

This process ensures we eventually arrive at the most simplified and direct form of the variable's value, making it easy to understand and verify.