Math worksheet for solving equations with variables on both sides, including an example and six problems to solve.

To solve these equations, we need to isolate the variable (like $n$, $a$, $x$, etc.) on one side of the equal sign. We do this by performing the same operation on both sides of the equation.

Here are the step-by-step solutions for each problem:

1. $n - 3n = 14 - 4n$
* Combine like terms on the left side: $n - 3n$ becomes $-2n$.
* Equation: $-2n = 14 - 4n$
* Move the variable to one side: Add $4n$ to both sides to cancel out the $-4n$.
* $-2n + 4n = 14$
* $2n = 14$
* Isolate the variable: Divide both sides by 2.
* $n = 7$

2. $7a + 3 = 4a - 18$
* Move the variables to one side: Subtract $4a$ from both sides.
* $7a - 4a + 3 = -18$
* $3a + 3 = -18$
* Move the constant to the other side: Subtract 3 from both sides.
* $3a = -18 - 3$
* $3a = -21$
* Isolate the variable: Divide both sides by 3.
* $a = -7$

3. $5x - 7 = -10x + 8$
* Move the variables to one side: Add $10x$ to both sides.
* $5x + 10x - 7 = 8$
* $15x - 7 = 8$
* Move the constant to the other side: Add 7 to both sides.
* $15x = 8 + 7$
* $15x = 15$
* Isolate the variable: Divide both sides by 15.
* $x = 1$

4. $4 - 7k = 1 - 6k$
* Move the variables to one side: Add $6k$ to both sides.
* $4 - 7k + 6k = 1$
* $4 - k = 1$
* Move the constant to the other side: Subtract 4 from both sides.
* $-k = 1 - 4$
* $-k = -3$
* Isolate the variable: Divide by -1 (or multiply by -1) to make $k$ positive.
* $k = 3$

5. $22 + 4a = 3a - 13$
* Move the variables to one side: Subtract $3a$ from both sides.
* $22 + 4a - 3a = -13$
* $22 + a = -13$
* Move the constant to the other side: Subtract 22 from both sides.
* $a = -13 - 22$
* $a = -35$

6. $6y - 9y - 4 = -2y - 2$
* Combine like terms on the left side: $6y - 9y$ becomes $-3y$.
* Equation: $-3y - 4 = -2y - 2$
* Move the variables to one side: Add $2y$ to both sides.
* $-3y + 2y - 4 = -2$
* $-y - 4 = -2$
* Move the constant to the other side: Add 4 to both sides.
* $-y = -2 + 4$
* $-y = 2$
* Isolate the variable: Divide by -1.
* $y = -2$

Final Answer:
1. $n = 7$
2. $a = -7$
3. $x = 1$
4. $k = 3$
5. $a = -35$
6. $y = -2$