91Ó°ÊÓ

Algebraic operations are the foundation of solving equations like the one shown in the exercise. These operations include addition, subtraction, multiplication, and division, which are used to manipulate the equation to find the value of the variable.

In the given problem, we see an example of how addition and division are used to solve a linear equation. Initially, we add 5 to both sides to remove the -5 attached to the 6x term. This is leveraging the principle that doing the same operation to both sides of the equation keeps it balanced.

After simplifying the equation, division comes into play to isolate the variable. We divide each side by 6 because 6x implies 6 multiplied by x. By dividing both terms by 6, we’re effectively reversing the multiplication operation, leaving us with x on one side of the equation, which is our aim.

Isolating variables is a technique used to solve for a single variable in terms of the others in an equation. This is typically done by performing algebraic operations that move all terms containing the variable to one side of the equation and all other terms to the opposite side.

When applying this to the exercise, the variable 'x' was isolated by first adding 5 to both sides of the equation to cancel out the -5 on the left side. This left the variable 'x' multiplied by 6, which is then dealt with by dividing both sides by 6. The goal is to have 'x' by itself on one side of the equation to find its value. Remember, each step must maintain the balance of the equation, as if you were balancing a scale. Anything done to one side must be done to the other.

Equation simplification involves reducing an equation to its simplest form to make it easier to solve. In the process of solving linear equations, we often simplify to remove brackets, combine like terms, and reduce fractions where possible.

Looking at our exercise, after adding 5 to both sides, the equation simplifies to exclude the constant term on the left side, leaving only the term with the variable. Dividing both sides by 6 simplifies the equation further to an isolated variable, 'x', with a simple numerical value, in this case, -4.

Simplifying an equation can sometimes be more complex, involving several steps of combining like terms, but the guiding principle remains: to make the equation as straightforward as possible while aiming to isolate the variable.