Question

algebra 1
week 6 solving practice
solve each equation.

1. 8 - 6v = 5v - 3
2. 5n - 6 = 6n + 1
3. 5x = x - 6x
4. 2k + 7k = 4 + 4k - 3 - 1
5. a + 2 = 14 + 3a
6. -3x = x + 8
7. 6b - 6 = 8(b + 1)
8. 39 + 2a = 7 + 8(4 + 8a)
9. -5 - p = -2(p + 3)
10. -39 + 6x = 7(6 + 4x) + 5x
11. 4 + 5a = 4(1 - 8a)
12. -5p + 3 = -2(p + 6)
13. -v + v = 4
14. 4n - 7 - 4n = 0
15. p - 8 - p = -6
16. -5p + 5p = -2
17. 0 = -2v + 2v
18. 8 - 7r + 7r = 13

Explanation:

Step1: Solve equation 1

8 - 6v = 5v - 3, add 6v to both sides:
8 = 5v - 3+6v, simplify to 8 = 11v - 3. Then add 3 to both sides: 8 + 3=11v, so 11 = 11v, and v = 1.

Step2: Solve equation 2

5n - 6 = 6n + 1, subtract 5n from both sides:

• 6=n + 1. Then subtract 1 from both sides: n=-7.

Step3: Solve equation 3

5x=x - 6x, simplify the right - hand side: 5x=-5x. Add 5x to both sides: 10x = 0, so x = 0.

Step4: Solve equation 4

2k + 7k=4 + 4k-3 - 1, simplify both sides. Left - hand side: 9k, right - hand side: 4k. So 9k=4k, subtract 4k from both sides: 5k = 0, k = 0.

Step5: Solve equation 5

a + 2=14 + 3a, subtract a from both sides:
2 = 14+2a. Then subtract 14 from both sides: - 12 = 2a, so a=-6.

Step6: Solve equation 6

• 3x=x + 8, subtract x from both sides:
• 4x = 8. Divide both sides by - 4: x=-2.

Step7: Solve equation 7

6b - 6 = 8(b + 1), expand the right - hand side: 6b - 6 = 8b+8. Subtract 6b from both sides: - 6 = 2b + 8. Then subtract 8 from both sides: - 14 = 2b, so b=-7.

Step8: Solve equation 8

39 + 2a=7 + 8(4 + 8a), expand the right - hand side: 39 + 2a=7 + 32+64a, simplify to 39 + 2a=39 + 64a. Subtract 2a from both sides: 39 = 39+62a. Subtract 39 from both sides: 62a = 0, so a = 0.

Step9: Solve equation 9

• 5 - p=-2(p + 3), expand the right - hand side: - 5 - p=-2p - 6. Add 2p to both sides: - 5 + p=-6. Then add 5 to both sides: p=-1.

Step10: Solve equation 10

• 39 + 6x=7(6 + 4x)+5x, expand the right - hand side: - 39 + 6x=42 + 28x+5x, simplify to - 39 + 6x=42 + 33x. Subtract 6x from both sides: - 39 = 42 + 27x. Then subtract 42 from both sides: - 81 = 27x, so x=-3.

Step11: Solve equation 11

4 + 5a=4(1 - 8a), expand the right - hand side: 4 + 5a=4 - 32a. Subtract 4 from both sides: 5a=-32a. Add 32a to both sides: 37a = 0, so a = 0.

Step12: Solve equation 12

• 5p + 3=-2(p + 6), expand the right - hand side: - 5p + 3=-2p - 12. Add 2p to both sides: - 3p + 3=-12. Then subtract 3 from both sides: - 3p=-15, so p = 5.

Step13: Solve equation 13

• v + v = 4, simplify the left - hand side: 0 = 4, no solution.

Step14: Solve equation 14

4n - 7 - 4n = 0, simplify the left - hand side: - 7 = 0, no solution.

Step15: Solve equation 15

p - 8 - p=-6, simplify the left - hand side: - 8=-6, no solution.

Step16: Solve equation 16

• 5p + 5p=-2, simplify the left - hand side: 0=-2, no solution.

Step17: Solve equation 17

0=-2v + 2v, simplify the right - hand side: 0 = 0, all real numbers are solutions.

Step18: Solve equation 18

8 - 7r+7r = 13, simplify the left - hand side: 8 = 13, no solution.

Answer:

1. v = 1
2. n=-7
3. x = 0
4. k = 0
5. a=-6
6. x=-2
7. b=-7
8. a = 0
9. p=-1
10. x=-3
11. a = 0
12. p = 5
13. No solution
14. No solution
15. No solution
16. No solution
17. All real numbers are solutions
18. No solution