Solve for x Worksheet for 5th - 10th Grade | Lesson Planet - Free Printable

I have solved all 10 equations from the worksheet. Below is the step-by-step reasoning for each problem, followed by the final answers.

Problem 1:
Equation: $-4(8 - 6r) = 35$
1. Divide both sides by -4: $8 - 6r = 35 / -4 = -8.75$
2. Subtract 8 from both sides: $-6r = -8.75 - 8 = -16.75$
3. Divide by -6: $r = -16.75 / -6 \approx 2.7916...$
4. Round to nearest hundredth: $2.79$

Problem 2:
Equation: $2 - 9(1 - 4x) = -24$
1. Distribute the -9: $2 - 9 + 36x = -24$
2. Combine constants: $-7 + 36x = -24$
3. Add 7 to both sides: $36x = -17$
4. Divide by 36: $x = -17 / 36 \approx -0.4722...$
5. Round to nearest hundredth: $-0.47$

Problem 3:
Equation: $4(9v + 5) = -32 + 6v$
1. Distribute the 4: $36v + 20 = -32 + 6v$
2. Subtract $6v$ from both sides: $30v + 20 = -32$
3. Subtract 20 from both sides: $30v = -52$
4. Divide by 30: $v = -52 / 30 \approx -1.7333...$
5. Round to nearest hundredth: $-1.73$

Problem 4:
Equation: $-2(1 + 7k) = -20$
1. Divide both sides by -2: $1 + 7k = 10$
2. Subtract 1 from both sides: $7k = 9$
3. Divide by 7: $k = 9 / 7 \approx 1.2857...$
4. Round to nearest hundredth: $1.29$

Problem 5:
Equation: $-8(5d - 2) = -25$
1. Distribute the -8: $-40d + 16 = -25$
2. Subtract 16 from both sides: $-40d = -41$
3. Divide by -40: $d = -41 / -40 = 1.025$
4. Round to nearest hundredth: $1.03$

Problem 6:
Equation: $-16 = 3(6h + 5)$
1. Distribute the 3: $-16 = 18h + 15$
2. Subtract 15 from both sides: $-31 = 18h$
3. Divide by 18: $h = -31 / 18 \approx -1.7222...$
4. Round to nearest hundredth: $-1.72$

Problem 7:
Equation: $19 = 7z - 2z$
1. Combine like terms on the right: $19 = 5z$
2. Divide by 5: $z = 19 / 5 = 3.8$
3. Written as hundredth: $3.80$

Problem 8:
Equation: $2b + 7 + 8b = 35$
1. Combine like terms ($2b + 8b$): $10b + 7 = 35$
2. Subtract 7 from both sides: $10b = 28$
3. Divide by 10: $b = 2.8$
4. Written as hundredth: $2.80$

Problem 9:
Equation: $-35 = 5 + 7(a + 2)$
1. Distribute the 7: $-35 = 5 + 7a + 14$
2. Combine constants on right ($5 + 14$): $-35 = 19 + 7a$
3. Subtract 19 from both sides: $-54 = 7a$
4. Divide by 7: $a = -54 / 7 \approx -7.7142...$
5. Round to nearest hundredth: $-7.71$

Problem 10:
Equation: $-6s - 2 + 3 = -35$
1. Combine constants on left ($-2 + 3$): $-6s + 1 = -35$
2. Subtract 1 from both sides: $-6s = -36$
3. Divide by -6: $s = 6$
4. Written as hundredth: $6.00$

Final Answer:
1) 2.79
2) -0.47
3) -1.73
4) 1.29
5) 1.03
6) -1.72
7) 3.80
8) 2.80
9) -7.71
10) 6.00