Pre-Algebra Worksheets | Equations Worksheets - Free Printable

Here are the step-by-step solutions for each equation on the worksheet.

1) $\frac{12 + a}{-17} = -18$
* Multiply both sides by $-17$:
$12 + a = -18 \times -17$
$12 + a = 306$
* Subtract $12$ from both sides:
$a = 306 - 12$
$a = 294$

2) $\frac{s + 6}{17} = 18$
* Multiply both sides by $17$:
$s + 6 = 18 \times 17$
$s + 6 = 306$
* Subtract $6$ from both sides:
$s = 306 - 6$
$s = 300$

3) $\frac{y + 20}{-21} = -3$
* Multiply both sides by $-21$:
$y + 20 = -3 \times -21$
$y + 20 = 63$
* Subtract $20$ from both sides:
$y = 63 - 20$
$y = 43$

4) $\frac{z - 23}{6} = -25$
* Multiply both sides by $6$:
$z - 23 = -25 \times 6$
$z - 23 = -150$
* Add $23$ to both sides:
$z = -150 + 23$
$z = -127$

5) $\frac{15 - f}{-18} = -23$
* Multiply both sides by $-18$:
$15 - f = -23 \times -18$
$15 - f = 414$
* Subtract $15$ from both sides:
$-f = 414 - 15$
$-f = 399$
* Divide by $-1$ (or multiply by $-1$):
$f = -399$

6) $-21r + 25 = -18$
* Subtract $25$ from both sides:
$-21r = -18 - 25$
$-21r = -43$
* Divide by $-21$:
$r = \frac{-43}{-21}$
$r \approx 2.0476...$
* Round to the nearest hundredth:
$r \approx 2.05$

7) $\frac{28 - v}{25} = 29$
* Multiply both sides by $25$:
$28 - v = 29 \times 25$
$28 - v = 725$
* Subtract $28$ from both sides:
$-v = 725 - 28$
$-v = 697$
* Divide by $-1$:
$v = -697$

8) $-15 - 2k = -5$
* Add $15$ to both sides:
$-2k = -5 + 15$
$-2k = 10$
* Divide by $-2$:
$k = \frac{10}{-2}$
$k = -5$

9) $\frac{b - 11}{-29} = -18$
* Multiply both sides by $-29$:
$b - 11 = -18 \times -29$
$b - 11 = 522$
* Add $11$ to both sides:
$b = 522 + 11$
$b = 533$

10) $-13 + \frac{7}{8}x = 5$
* Add $13$ to both sides:
$\frac{7}{8}x = 5 + 13$
$\frac{7}{8}x = 18$
* Multiply both sides by $\frac{8}{7}$ (the reciprocal) to isolate $x$:
$x = 18 \times \frac{8}{7}$
$x = \frac{144}{7}$
$x \approx 20.5714...$
* Round to the nearest hundredth:
$x \approx 20.57$

Final Answer:
1) a = 294
2) s = 300
3) y = 43
4) z = -127
5) f = -399
6) r ≈ 2.05
7) v = -697
8) k = -5
9) b = 533
10) x ≈ 20.57