Here are the step-by-step solutions for each equation on the worksheet.
1) $9c + 1 = 10$
* Subtract 1 from both sides: $9c = 9$
* Divide by 9: $c = 1$
2) $6y - 5 = 7$
* Add 5 to both sides: $6y = 12$
* Divide by 6: $y = 2$
3) $8 = 3a - 4$
* Add 4 to both sides: $12 = 3a$
* Divide by 3: $4 = a$ (or $a = 4$)
4) $\frac{m}{5} + 9 = 11$
* Subtract 9 from both sides: $\frac{m}{5} = 2$
* Multiply by 5: $m = 10$
5) $13 + 7x = 27$
* Subtract 13 from both sides: $7x = 14$
* Divide by 7: $x = 2$
6) $17 - q = 6$
* Subtract 17 from both sides: $-q = -11$
* Divide by -1 (or just flip the signs): $q = 11$
7) $\frac{n - 31}{4} = 2$
* Multiply both sides by 4: $n - 31 = 8$
* Add 31 to both sides: $n = 39$
8) $1 + 2r = 35$
* Subtract 1 from both sides: $2r = 34$
* Divide by 2: $r = 17$
9) $42 + 5t = 8t$
* Subtract $5t$ from both sides to group the variables: $42 = 3t$
* Divide by 3: $14 = t$ (or $t = 14$)
10) $4p - 3 = 17$
* Add 3 to both sides: $4p = 20$
* Divide by 4: $p = 5$
Final Answer:
1) c = 1
2) y = 2
3) a = 4
4) m = 10
5) x = 2
6) q = 11
7) n = 39
8) r = 17
9) t = 14
10) p = 5
Parent Tip: Review the logic above to help your child master the concept of solve for x worksheets.
