Solve: (-2/3x)-(-7⅔x) | Combining Like Terms with Negative Fractions

Question

Solve the following exercise:

(23x)(763x)= (-\frac{2}{3}x)-(-7\frac{6}{3}x)=

Step-by-Step Solution

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

(x)=+x -(-x)=+x

This leaves us with the exercise:

23x+763x= -\frac{2}{3}x+7\frac{6}{3}x=

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

763x=7×3+63x=21+63x=273x=9x 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:

23x+9x= -\frac{2}{3}x+9x=

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

9x23x=813x 9x-\frac{2}{3}x=8\frac{1}{3}x

Answer

813x 8\frac{1}{3}x