Question

Solve each equation for the missing variable. If your answer is not an integer, write it as an improper fraction.

Answer 1

To start the problem, you will want to move the numbers with variables and the ones without to the other side, then combine them together so that there is only one thing on each side. Then divide on both sides by the variable's coefficient and you will get your answer. Here is it done for the 1st problem.
$5n - 14 = 8n + 4 \\ 5n - 14 - 5n = 8n + 4 - 5n \\ - 14 = 3n + 4 \\ - 14 - 4 = 3n + 4 - 4 \\ - 18 = 3n \\ \frac{3}{3} n = \frac{ - 18}{6} \\ n = - 6$
For the second one you will want to start by simplifying everything on both sides since you can combine the constants (numbers without any variables). It should look like this:
$- 15 + 4 - 5a = - 2 + 26 + 30a \\ - 11 - 5a = 24 + 30a$
What you can do from here is push constants to one side and variables to the other like before. Here is how it would look:
$- 11 - 5a = 24 + 30a \\ - 11 - 5a - 24 = 24 - 24 + 30a \\ - 35 - 5a = 30a \\ - 35 - 5a + 5a = 30a + 5a \\ - 35 = 35a$
Once there is only one thing on both side, you can divide both sides by the coefficient (the number attached to a variable) to get the variable alone.
$35a = - 35 \\ \frac{35}{35} a = \frac{ - 35}{35} \\ a = - 1$
Thus, a is equal to -1.

For the third problem, it is more of the same type of problem that we have done before. Since there are no multiples of anything (variables or constants) on each side, we can start pushing variables to one side and constants to the others like so:
$- 8x + 25 = 3 - 9x \\ - 8x + 9x + 25 = 3 - 9x + 9x \\ x + 25 = 3 \\ x + 25 - 25 = 3 - 25 \\ x = - 22$
Since x's coefficient is 1, there is no need to divide and your answer is -22.

Answer 2

First example:

Subtract the 8n on both sides to get the variable on one side of the equation. Do the same for the regular numbers. Then divide by -3.

$5n-14=8n+4\\ \\ 5n-8n=4+14 \\ \\ -3n=18\\ \\ n=-6$

This should be your final answer.

Second Example:

Do the same thing as explained in Example 1. Here's some work to help guide you.

$-15 - 5a + 4 = -2 + 30a + 26\\ \\ -5a-30a=-2+26+15\\ \\ -35a=39\\ \\ a = \frac{39}{-35}$

That should be your final answer here.

Third Example:

$3 - 9x = -8x + 25\\ \\ -9x+8x=25-3\\ \\ -x=22\\ \\ x=-22$

Hope this helps and its understandable! Let me know if you still don't understand.