Simplify 6/7*(x-2)

Solution:

Step 1:

Utilize the distributive property to expand the expression: $\frac{6}{7} \cdot (x) + \frac{6}{7} \cdot (-2)$.

Step 2:

Simplify the multiplication of $\frac{6}{7}$ with $x$: $\frac{6x}{7} + \frac{6}{7} \cdot (-2)$.

Step 3:

Proceed to multiply $\frac{6}{7}$ with $-2$.

Step 3.1:

Combine the fraction $\frac{6}{7}$ with the number $-2$: $\frac{6x}{7} + \frac{6 \cdot (-2)}{7}$.

Step 3.2:

Execute the multiplication of $6$ and $-2$: $\frac{6x}{7} + \frac{-12}{7}$.

Step 4:

Reposition the negative sign to the front of the fraction: $\frac{6x}{7} - \frac{12}{7}$.

Knowledge Notes:

The distributive property is a fundamental algebraic property used to simplify expressions. It states that for any numbers a, b, and c, the following is true: a(b + c) = ab + ac.

In the context of this problem, the distributive property is applied to the expression 6/7 * (x - 2), which involves a fraction (6/7) being distributed over the addition within the parentheses (x - 2).

When simplifying expressions involving fractions and variables, it is important to apply the distributive property correctly and to perform multiplication and addition operations with care, especially when dealing with negative numbers.

The final step often involves simplifying the expression to its simplest form, which may include combining like terms or repositioning negative signs for clarity.

In this problem, after applying the distributive property, we multiply the fraction 6/7 by each term inside the parentheses separately. The multiplication of a fraction with a variable or a number is done by multiplying the numerator of the fraction with the variable or number while keeping the denominator unchanged.

When multiplying a negative number by a fraction, the negative sign can be associated either with the numerator or the entire fraction. In the final expression, it is conventional to place the negative sign in front of the fraction for clarity.