Multiplication and Division of Signed Mumbers: Solving the problem

Since we are multiplying two positive numbers, the result will necessarily be positive.

$+\times+=+$

Therefore:

$+10\times+3=+30$

Due to the fact that we are multiplying a positive number by a negative number, the result must be a negative number:

$+\times-=-$

Therefore:

$+9\times-4=-36$

First, we'll perform the operations 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:

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