Multiplication and Division of Signed Mumbers: Using variables

First, we'll perform the operations inside of the parentheses, remembering the rule:

$-(-x)=+x$

This leaves us with the exercise:

$-\frac{2}{3}x+7\frac{6}{3}x=$

Now we'll address the mixed fraction and convert it into an improper fraction:

$7\frac{6}{3}x=\frac{7\times3+6}{3}x=\frac{21+6}{3}x=\frac{27}{3}x=9x$

Now we have the exercise:

$-\frac{2}{3}x+9x=$

Finally, we'll use the distributive property to get the answer:

$9x-\frac{2}{3}x=8\frac{1}{3}x$

Let's solve this problem step-by-step:

• Step 1: Multiply the coefficients: Take the coefficients of the terms $+4$ and $-4$. Multiplying these, we get $4 \times -4 = -16$.
• Step 2: Multiply the variables: The term contains the variable $x$. Using the property of exponents, $x^1 \times x^1 = x^{1+1} = x^2$.
• Step 3: Write the combined expression: Combine the outcomes from Steps 1 and 2: $-16x^2$.

Hence, the expression $(+4x)\times(-4x)$ simplifies to $-16x^2$.

Therefore, the correct solution to the problem is $-16x^2$.

Note that in the first stage we are dividing a positive number by a negative number:

$+:-=-$

Now the exercise is:

$-:a?0$

Since we don't know whether a is a positive or negative number, we cannot determine the sign.