Your question presented was: [tex]\frac{2}{5} (\frac{1}{3} x-\frac{15}{8} )-\frac{1}{3} (\frac{1}{2} -\frac{2}{3}x)[/tex]
Okay, lets distribute this problem and break it into two parts. We will distribute 2/5 and -1/3 to the numbers in parenthesis. This is the distributive property.
Step 1.
[tex]\frac{2}{5} (\frac{1}{3} x-\frac{15}{8} )[/tex] when distributed is [tex]\frac{2}{15} x - \frac{30}{40}[/tex]
Please note that -1/3 can be rewritten as + -1/3. So you must distribute the negative.
Step 2.
[tex]\frac{-1}{5} + \frac{2}{9} x[/tex]
So..lets put the 2 parts of the equation together
[tex]\frac{2}{15} x - \frac{30}{40}[/tex] + [tex]\frac{-1}{5} + \frac{2}{9} x[/tex] can be simplified by getting the common denominator.
You can only add like terms, so those fractions with x can only be combined with x.
Step 3.
Lets reformat while we're at it
[tex]\frac{6}{45} x + \frac{10}{45} x -\frac{30}{40} -\frac{8}{40}[/tex]
We got 45 because the LCM (Lowest Common Multiple) of 15 and 9 was 45. We multiplied both sides of the fraction by 3 for 2/15x and we multiplied by 5 on both parts of the fraction for 2/9x.
Now we combine.
Step 4.
[tex]\frac{16}{45}x-\frac{38}{40}[/tex]. We can still simplify!
Step 5.
-38/40 can be simplified by a common factor, 2! So our final answer is
[tex]\frac{16}{45}x-\frac{19}{20}[/tex]
I hope this helps you, heart if it helps.
