Simplify (8-6x)/-3

Solution:

Simplification Process:

Step 1:

Extract the common factor of $2$ from the terms $8$ and $-6x$.

Step 1.1:

Take $2$ out of $8$. Write it as $\frac{2(4)-6x}{-3}$.

Step 1.2:

Extract $2$ from the term $-6x$. It becomes $\frac{2(4)+2(-3x)}{-3}$.

Step 1.3:

Combine the factored terms. The expression simplifies to $\frac{2(4-3x)}{-3}$.

Step 2:

Relocate the negative sign to the front of the fraction to get $-\frac{2(4-3x)}{3}$.

Knowledge Notes:

The process of simplifying an algebraic expression often involves factoring out common terms to reduce the expression to its simplest form. Here are the relevant knowledge points:

1. Factoring: This is the process of breaking down an expression into its constituent factors. In this case, we factored out a $2$ from both terms in the numerator.

2. Simplifying Fractions: When simplifying fractions, we aim to reduce them to their simplest form by eliminating common factors in the numerator and denominator.

3. Negative Signs: A negative sign in front of a fraction can be distributed across the numerator or the denominator, but not both. It indicates the opposite value of the fraction.

4. Algebraic Manipulation: This involves rearranging and simplifying expressions using algebraic rules, such as the distributive property, which in this case allowed us to factor out the $2$.

5. LaTeX Formatting: In the solution, LaTeX is used to format mathematical expressions for clarity. For instance, $\frac{2(4-3x)}{-3}$ is a LaTeX-formatted fraction.

By understanding these concepts, one can effectively simplify algebraic expressions and solve a variety of mathematical problems.