Answer: Refer to the screenshot below
I've filled in the boxes with the proper answers
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Explanation for problem 1
In line 1, I used the distributive rule a*(b+c) = a*b+a*c. On the left side the 3(n+2) becomes 3n+6. On the right side, the 9(6-n) becomes 54-9n
On the next line, I added 9n to both sides. The 3n on the left side updates to 3n+9n = 12n.
For the third line, I subtracted 6 from both sides. Then the last line involves dividing both sides by 12 to fully isolate n. To confirm the solution n = 4, plug it back into the original equation. You should get the same thing on both sides after simplifying.
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Explanation for problem 2
The steps here are similar as problem 1, but this time we're involving fractions. Unfortunately, these steps don't involve clearing out the fractions which is often a handy trick to use.
We use the distributive rule on line 1
For line 2, we subtract 2m/9 from both sides. Think of 2m/3 as 6m/9 to help combine the fractions. The denominators must be the same for you to be able to add or subtract fractions.
For line 3, we subtract 4/3 from both sides. Think of 4/3 as 12/9.
The last step is to multiply both sides by 9/4, which is the reciprocal of 4/9. Your teacher made a typo on the right hand side of the last line. It should read [tex]\frac{4}{9}m[/tex] and not [tex]\frac{2}{9}m[/tex]. Refer to the previous line.
