91Ó°ÊÓ

When solving linear equations, the first step is often isolating the variable you're solving for. The goal here is to get the variable alone on one side of the equation so you can easily determine its value.
In our given exercise, we have the equation \(3x = 51\). To isolate the variable, we need to remove any coefficients attached to it. Here, '3' is multiplied by 'x'.
To undo this multiplication, we use division, and we divide both sides of the equation by 3. The equation then looks like: \[x = \frac{51}{3}\]. We did this to ensure that 'x' is by itself on one side, making it much simpler to solve for 'x'.
Keep in mind that whatever operation you do to one side of the equation, you must do to the other to keep the balance.

After isolating the variable, we often need to simplify fractions. It is a critical step to finding a clear and understandable solution.
In the exercise, once we have the equation \[x = \frac{51}{3}\], we need to simplify this fraction.
Simplifying means dividing 51 by 3, which equals 17. Therefore, we find \x = 17\.
For fractions, always look to see if the numerator (top number) is divisible by the denominator (bottom number). If it is, perform the division and write the result as a whole number or a simpler fraction. This makes complex equations easier to manage and understand.

After solving for a variable, it's important to verify your solution. This ensures that the value you found is accurate and satisfies the original equation.
For our problem, after finding \(x = 17\), we substitute it back into the original equation to check it:
Original equation: \(3x = 51\)
Substitute \(x = 17\): \(3(17) = 51\)
Calculate the left side: \(51 = 51\)
Since both sides of the equation are equal, our solution is correct.
This verification step guarantees that no mistakes were made during the process and confirms that our answer is the true solution to the equation.