Solve Linear Equations worksheet with practice problems for algebra students.

Here are the step-by-step solutions for each equation. To solve these, we want to get $x$ by itself. We do this by "undoing" the operations in reverse order: first multiply to remove fractions, then add or subtract numbers, and finally divide by the number attached to $x$.

1. $\frac{6x + 5}{5} = 7$
* Multiply both sides by 5: $6x + 5 = 35$
* Subtract 5 from both sides: $6x = 30$
* Divide by 6: $x = 5$

2. $9 = \frac{4x - 5}{3}$
* Multiply both sides by 3: $27 = 4x - 5$
* Add 5 to both sides: $32 = 4x$
* Divide by 4: $8 = x$ (or $x = 8$)

3. $\frac{5x - 5}{5} = 6$
* Multiply both sides by 5: $5x - 5 = 30$
* Add 5 to both sides: $5x = 35$
* Divide by 5: $x = 7$

4. $\frac{7x - 5}{5} = 6$
* Multiply both sides by 5: $7x - 5 = 30$
* Add 5 to both sides: $7x = 35$
* Divide by 7: $x = 5$

5. $5 = \frac{6x + 2}{4}$
* Multiply both sides by 4: $20 = 6x + 2$
* Subtract 2 from both sides: $18 = 6x$
* Divide by 6: $3 = x$ (or $x = 3$)

6. $\frac{4x + 8}{4} = 6$
* Multiply both sides by 4: $4x + 8 = 24$
* Subtract 8 from both sides: $4x = 16$
* Divide by 4: $x = 4$

7. $\frac{6x + 9}{3} = 13$
* Multiply both sides by 3: $6x + 9 = 39$
* Subtract 9 from both sides: $6x = 30$
* Divide by 6: $x = 5$

8. $2 = \frac{3x - 2}{5}$
* Multiply both sides by 5: $10 = 3x - 2$
* Add 2 to both sides: $12 = 3x$
* Divide by 3: $4 = x$ (or $x = 4$)

Final Answer:
1. $x = 5$
2. $x = 8$
3. $x = 7$
4. $x = 5$
5. $x = 3$
6. $x = 4$
7. $x = 5$
8. $x = 4$