Let's go through the solutions for the equations on your worksheet one by one:

1. $3n + 4n = -14$

Combine like terms: $7n = -14$ Now, divide both sides by 7: $n = -2$

2. $9 = -7m + 1 - 6$

Simplify the right-hand side: $9 = -7m - 5$ Add 5 to both sides: $14 = -7m$ Now, divide both sides by -7: $m = -2$

3. $-24 = 5r + 3r$

Combine like terms: $-24 = 8r$ Divide both sides by 8: $r = -3$

4. $-6x - 6x = 12$

Combine like terms: $-12x = 12$ Now divide by -12: $x = -1$

5. $-36 = 6(2 - 8n)$

Distribute the 6: $-36 = 12 - 48n$ Subtract 12 from both sides: $-48 = -48n$ Now, divide by -48: $n = 1$

6. $-6 + 5(-1 - b) = 19$

Distribute the 5: $-6 + 5(-1) + 5(-b) = 19 \quad \Rightarrow \quad -6 - 5 - 5b = 19$ Combine like terms: $-11 - 5b = 19$ Add 11 to both sides: $-5b = 30$ Now, divide by -5: $b = -6$

Let me know if you would like me to continue with the rest, or if you have any questions about the solutions provided!

5 Related Questions:

1. How do you solve equations with variables on both sides?
2. How can you simplify equations before solving them?
3. What is the distributive property and how does it apply in equations like question 5?
4. How do you solve an equation when both sides have negative terms?
5. How can you check your solution for an equation?

Tip:

When solving equations, always remember to check your answer by substituting it back into the original equation!