Solve the Equations worksheet with ten algebra problems for practice.

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

1) $-4(8 - 6r) = 35$
* Distribute the $-4$ into the parentheses: $-32 + 24r = 35$
* Add $32$ to both sides: $24r = 67$
* Divide by $24$: $r = 67 / 24$
* $r \approx 2.79$

2) $2 - 9(1 - 4x) = -24$
* Distribute the $-9$ into the parentheses: $2 - 9 + 36x = -24$
* Combine like terms ($2 - 9$): $-7 + 36x = -24$
* Add $7$ to both sides: $36x = -17$
* Divide by $36$: $x = -17 / 36$
* $x \approx -0.47$

3) $4(9v + 5) = -32 + 6v$
* Distribute the $4$ on the left side: $36v + 20 = -32 + 6v$
* Subtract $6v$ from both sides: $30v + 20 = -32$
* Subtract $20$ from both sides: $30v = -52$
* Divide by $30$: $v = -52 / 30$
* $v \approx -1.73$

4) $-2(1 + 7k) = -20$
* Distribute the $-2$: $-2 - 14k = -20$
* Add $2$ to both sides: $-14k = -18$
* Divide by $-14$: $k = -18 / -14$
* $k \approx 1.29$

5) $-8(5d - 2) = -25$
* Distribute the $-8$: $-40d + 16 = -25$
* Subtract $16$ from both sides: $-40d = -41$
* Divide by $-40$: $d = -41 / -40$
* $d = 1.025$, which rounds to $1.03$

6) $-16 = 3(6h + 5)$
* Distribute the $3$: $-16 = 18h + 15$
* Subtract $15$ from both sides: $-31 = 18h$
* Divide by $18$: $h = -31 / 18$
* $h \approx -1.72$

7) $19 = 7z - 2z$
* Combine like terms on the right side ($7z - 2z$): $19 = 5z$
* Divide by $5$: $z = 19 / 5$
* $z = 3.8$

8) $2b + 7 + 8b = 35$
* Combine like terms on the left side ($2b + 8b$): $10b + 7 = 35$
* Subtract $7$ from both sides: $10b = 28$
* Divide by $10$: $b = 2.8$

9) $-35 = 5 + 7(a + 2)$
* Distribute the $7$: $-35 = 5 + 7a + 14$
* Combine constants on the right side ($5 + 14$): $-35 = 19 + 7a$
* Subtract $19$ from both sides: $-54 = 7a$
* Divide by $7$: $a = -54 / 7$
* $a \approx -7.71$

10) $-6s - 2 + 3 = -35$
* Combine constants on the left side ($-2 + 3$): $-6s + 1 = -35$
* Subtract $1$ from both sides: $-6s = -36$
* Divide by $-6$: $s = 6$

Final Answer:
1) r ≈ 2.79
2) x ≈ -0.47
3) v ≈ -1.73
4) k ≈ 1.29
5) d ≈ 1.03
6) h ≈ -1.72
7) z = 3.8
8) b = 2.8
9) a ≈ -7.71
10) s = 6