91Ó°ÊÓ

When solving linear equations, the goal is to get the variable on one side of the equation and the constants on the other. In the given exercise, we started with the equation:
\(21 + 6f = 7f + 14\).
To simplify this, we need to eliminate the variable term on one side. This is done by subtracting the variable term from both sides. In this case, we subtract \(6f\) from both sides:
\[21 + 6f - 6f = 7f + 14 - 6f\]
This simplification helps to move all the terms with the variable to one side, making it easier to solve the equation. It is crucial to always perform the same operation on both sides of the equation to maintain equality. After performing the subtraction, the equation simplifies to:
\[21 = f + 14\].

Isolating the variable means rearranging the equation so that the variable is on one side of the equation by itself. From the simplified equation \(21 = f + 14\), our goal is to solve for \(f\).
To isolate \(f\), we can subtract 14 from both sides of the equation:
\[21 - 14 = f + 14 - 14\]
By subtracting 14 from both sides, we are left with:
\[7 = f\].
Thus, the variable \(f\) is now isolated and we have found its value. This process ensures that we have a clear solution where the variable is by itself. Always remember to perform the same operation on both sides of the equation to maintain equality.

Simplifying equations involves combining like terms and performing basic arithmetic operations to make the equation easier to solve. In this exercise, the equation \(21 + 6f = 7f + 14\) was first simplified by subtracting \(6f\) from both sides, which resulted in:
\[21 = f + 14\].
Next, to further simplify, we isolated the variable \(f\) by subtracting 14 from both sides, leading to the final simplified equation:
\[7 = f\].
Throughout the process, we combined like terms and performed operations on both sides of the equation. This methodical approach transforms a more complex equation into a simple, solvable form. Simplifying equations is a key step in solving linear equations, as it helps clearly identify the value of the variable.