Worksheet for solving one-variable linear equations with fractions, designed for educational practice.

Here are the step-by-step solutions for all 15 problems on the worksheet.

1. $\frac{x}{3} + 3 = 6$
* Subtract 3 from both sides: $\frac{x}{3} = 3$
* Multiply both sides by 3: $x = 9$

2. $\frac{x}{7} + 3 = \frac{23}{7}$
* Convert 3 to a fraction with denominator 7: $3 = \frac{21}{7}$
* Equation becomes: $\frac{x}{7} + \frac{21}{7} = \frac{23}{7}$
* Subtract $\frac{21}{7}$ from both sides: $\frac{x}{7} = \frac{2}{7}$
* Multiply both sides by 7: $x = 2$

3. $\frac{x}{8} + 3 = \frac{13}{4}$
* Convert 3 to a fraction with denominator 4: $3 = \frac{12}{4}$
* Equation becomes: $\frac{x}{8} + \frac{12}{4} = \frac{13}{4}$
* Subtract $\frac{12}{4}$ from both sides: $\frac{x}{8} = \frac{1}{4}$
* Multiply both sides by 8: $x = \frac{8}{4} = 2$

4. $\frac{x}{5} + 8 = \frac{44}{5}$
* Convert 8 to a fraction with denominator 5: $8 = \frac{40}{5}$
* Equation becomes: $\frac{x}{5} + \frac{40}{5} = \frac{44}{5}$
* Subtract $\frac{40}{5}$ from both sides: $\frac{x}{5} = \frac{4}{5}$
* Multiply both sides by 5: $x = 4$

5. $\frac{x}{5} - 6 = -5$
* Add 6 to both sides: $\frac{x}{5} = 1$
* Multiply both sides by 5: $x = 5$

6. $\frac{x}{8} + 2 = \frac{25}{8}$
* Convert 2 to a fraction with denominator 8: $2 = \frac{16}{8}$
* Equation becomes: $\frac{x}{8} + \frac{16}{8} = \frac{25}{8}$
* Subtract $\frac{16}{8}$ from both sides: $\frac{x}{8} = \frac{9}{8}$
* Multiply both sides by 8: $x = 9$

7. $\frac{x}{7} + 6 = \frac{47}{7}$
* Convert 6 to a fraction with denominator 7: $6 = \frac{42}{7}$
* Equation becomes: $\frac{x}{7} + \frac{42}{7} = \frac{47}{7}$
* Subtract $\frac{42}{7}$ from both sides: $\frac{x}{7} = \frac{5}{7}$
* Multiply both sides by 7: $x = 5$

8. $\frac{x}{7} - 7 = -\frac{41}{7}$
* Convert -7 to a fraction with denominator 7: $-7 = -\frac{49}{7}$
* Equation becomes: $\frac{x}{7} - \frac{49}{7} = -\frac{41}{7}$
* Add $\frac{49}{7}$ to both sides: $\frac{x}{7} = \frac{8}{7}$
* Multiply both sides by 7: $x = 8$

9. $\frac{x}{8} - 8 = -7$
* Add 8 to both sides: $\frac{x}{8} = 1$
* Multiply both sides by 8: $x = 8$

10. $\frac{x}{3} + 5 = \frac{20}{3}$
* Convert 5 to a fraction with denominator 3: $5 = \frac{15}{3}$
* Equation becomes: $\frac{x}{3} + \frac{15}{3} = \frac{20}{3}$
* Subtract $\frac{15}{3}$ from both sides: $\frac{x}{3} = \frac{5}{3}$
* Multiply both sides by 3: $x = 5$

11. $\frac{x}{3} - 7 = -\frac{17}{3}$
* Convert -7 to a fraction with denominator 3: $-7 = -\frac{21}{3}$
* Equation becomes: $\frac{x}{3} - \frac{21}{3} = -\frac{17}{3}$
* Add $\frac{21}{3}$ to both sides: $\frac{x}{3} = \frac{4}{3}$
* Multiply both sides by 3: $x = 4$

12. $\frac{x}{3} + 3 = \frac{14}{3}$
* Convert 3 to a fraction with denominator 3: $3 = \frac{9}{3}$
* Equation becomes: $\frac{x}{3} + \frac{9}{3} = \frac{14}{3}$
* Subtract $\frac{9}{3}$ from both sides: $\frac{x}{3} = \frac{5}{3}$
* Multiply both sides by 3: $x = 5$

13. $\frac{x}{8} - 5 = -\frac{19}{4}$
* Convert -5 to a fraction with denominator 4 (to match the right side): $-5 = -\frac{20}{4}$
* Equation becomes: $\frac{x}{8} - \frac{20}{4} = -\frac{19}{4}$
* Add $\frac{20}{4}$ to both sides: $\frac{x}{8} = \frac{1}{4}$
* Multiply both sides by 8: $x = \frac{8}{4} = 2$

14. $\frac{x}{6} - 6 = -\frac{16}{3}$
* Convert -6 to a fraction with denominator 3: $-6 = -\frac{18}{3}$
* Equation becomes: $\frac{x}{6} - \frac{18}{3} = -\frac{16}{3}$
* Add $\frac{18}{3}$ to both sides: $\frac{x}{6} = \frac{2}{3}$
* Multiply both sides by 6: $x = \frac{12}{3} = 4$

15. $\frac{x}{8} - 6 = -\frac{21}{4}$
* Convert -6 to a fraction with denominator 4: $-6 = -\frac{24}{4}$
* Equation becomes: $\frac{x}{8} - \frac{24}{4} = -\frac{21}{4}$
* Add $\frac{24}{4}$ to both sides: $\frac{x}{8} = \frac{3}{4}$
* Multiply both sides by 8: $x = \frac{24}{4} = 6$

Final Answer:
1. x = 9
2. x = 2
3. x = 2
4. x = 4
5. x = 5
6. x = 9
7. x = 5
8. x = 8
9. x = 8
10. x = 5
11. x = 4
12. x = 5
13. x = 2
14. x = 4
15. x = 6