Simplify (8-6x)/-3
The question is asking for the algebraic expression (8-6x)/-3 to be simplified, which means to rewrite the given expression in a more streamlined or reduced form without changing its value. This would involve carrying out the division by -3 on each term in the numerator, assuming no further context is given that might alter the expected operations.
$\frac{8 - 6 x}{- 3}$
Answer
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:
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.
Simplifying Fractions: When simplifying fractions, we aim to reduce them to their simplest form by eliminating common factors in the numerator and denominator.
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.
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 $2$.
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.
