determine the value of the unknown in each equation.\n1. -4 - 9p = 7p + 6\n2. 3w + 4 = 8w + 1\n3. 4 + 3z = 4…

determine the value of the unknown in each equation.\n1. -4 - 9p = 7p + 6\n2. 3w + 4 = 8w + 1\n3. 4 + 3z = 4 - 9z\n4. 6 + t = -9 + 2t\n5. -2(4 + 3j) - 1 = 6j\n6. -2(3f - 1) = 4f - 7\n7. -9 - 7q = 1 + 4q\n8. -8 - 8r = 4 - 2r\n9. -2(1 - 3v) = -6v - 5\n10. -4(1 + c) + 3 = -8c\n11. 7n - 2 = -7n - 8\n12. 9 - 7m = -1 + m\n13. 1 - 8k = 5k - 8\n14. -7h + 1 = -4h - 8\n15. 3 + 4s = 7 + 2s\n16. 1 - 9a = -1 + 6a\n17. 1 - 5d = -7 - 3d\n18. -9 + 7g = -g + 8\n19. -3(x - 3) = 2x + 9\n20. -y = 4(-y + 2) + 2

determine the value of the unknown in each equation.\n1. -4 - 9p = 7p + 6\n2. 3w + 4 = 8w + 1\n3. 4 + 3z = 4 - 9z\n4. 6 + t = -9 + 2t\n5. -2(4 + 3j) - 1 = 6j\n6. -2(3f - 1) = 4f - 7\n7. -9 - 7q = 1 + 4q\n8. -8 - 8r = 4 - 2r\n9. -2(1 - 3v) = -6v - 5\n10. -4(1 + c) + 3 = -8c\n11. 7n - 2 = -7n - 8\n12. 9 - 7m = -1 + m\n13. 1 - 8k = 5k - 8\n14. -7h + 1 = -4h - 8\n15. 3 + 4s = 7 + 2s\n16. 1 - 9a = -1 + 6a\n17. 1 - 5d = -7 - 3d\n18. -9 + 7g = -g + 8\n19. -3(x - 3) = 2x + 9\n20. -y = 4(-y + 2) + 2

Answer

  1. For the equation (-4 - 9p=7p + 6):
    • Step 1: Move variable - terms to one side
      • Add (9p) to both sides of the equation: (-4-9p + 9p=7p+9p + 6), which simplifies to (-4 = 16p+6).
    • Step 2: Move constant - terms to the other side
      • Subtract 6 from both sides: (-4 - 6=16p+6 - 6), resulting in (-10 = 16p).
    • Step 3: Solve for (p)
      • Divide both sides by 16: (p=\frac{-10}{16}=-\frac{5}{8}).
  2. For the equation (3w + 4=8w + 1):
    • Step 1: Move variable - terms to one side
      • Subtract (3w) from both sides: (3w-3w + 4=8w-3w + 1), giving (4 = 5w+1).
    • Step 2: Move constant - terms to the other side
      • Subtract 1 from both sides: (4 - 1=5w+1 - 1), so (3 = 5w).
    • Step 3: Solve for (w)
      • Divide both sides by 5: (w=\frac{3}{5}).
  3. For the equation (4 + 3z=4 - 9z):
    • Step 1: Move variable - terms to one side
      • Add (9z) to both sides: (4+3z + 9z=4-9z + 9z), resulting in (4 + 12z=4).
    • Step 2: Move constant - terms to the other side
      • Subtract 4 from both sides: (4 - 4+12z=4 - 4), so (12z = 0).
    • Step 3: Solve for (z)
      • Divide both sides by 12: (z = 0).
  4. For the equation (6 + t=-9 + 2t):
    • Step 1: Move variable - terms to one side
      • Subtract (t) from both sides: (6+t - t=-9+2t - t), giving (6=-9 + t).
    • Step 2: Move constant - terms to the other side
      • Add 9 to both sides: (6 + 9=-9 + 9+t), so (t = 15).
  5. For the equation (-2(4 + 3j)-1 = 6j):
    • Step 1: Expand the left - hand side
      • First, expand (-2(4 + 3j)) to get (-8-6j). Then the equation becomes (-8-6j-1 = 6j), or (-9-6j = 6j).
    • Step 2: Move variable - terms to one side
      • Add (6j) to both sides: (-9-6j+6j = 6j+6j), resulting in (-9 = 12j).
    • Step 3: Solve for (j)
      • Divide both sides by 12: (j=-\frac{9}{12}=-\frac{3}{4}).
  6. For the equation (-2(3f - 1)=4f-7):
    • Step 1: Expand the left - hand side
      • Expand (-2(3f - 1)) to get (-6f + 2). So the equation is (-6f + 2=4f-7).
    • Step 2: Move variable - terms to one side
      • Add (6f) to both sides: (-6f+6f + 2=4f+6f-7), giving (2 = 10f-7).
    • Step 3: Move constant - terms to the other side
      • Add 7 to both sides: (2 + 7=10f-7 + 7), so (9 = 10f).
    • Step 4: Solve for (f)
      • Divide both sides by 10: (f=\frac{9}{10}).
  7. For the equation (-9-7q = 1+4q):
    • Step 1: Move variable - terms to one side
      • Add (7q) to both sides: (-9-7q+7q = 1+4q+7q), resulting in (-9 = 1+11q).
    • Step 2: Move constant - terms to the other side
      • Subtract 1 from both sides: (-9 - 1=1 - 1+11q), so (-10 = 11q).
    • Step 3: Solve for (q)
      • Divide both sides by 11: (q=-\frac{10}{11}).
  8. For the equation (-8-8r = 4-2r):
    • Step 1: Move variable - terms to one side
      • Add (8r) to both sides: (-8-8r+8r = 4-2r+8r), giving (-8 = 4 + 6r).
    • Step 2: Move constant - terms to the other side
      • Subtract 4 from both sides: (-8 - 4=4 - 4+6r), so (-12 = 6r).
    • Step 3: Solve for (r)
      • Divide both sides by 6: (r=-2).
  9. For the equation (-2(1 - 3v)=-6v-5):
    • Step 1: Expand the left - hand side
      • Expand (-2(1 - 3v)) to get (-2 + 6v). Then the equation is (-2 + 6v=-6v-5).
    • Step 2: Move variable - terms to one side
      • Add (6v) to both sides: (-2+6v+6v=-6v+6v-5), resulting in (-2 + 12v=-5).
    • Step 3: Move constant - terms to the other side
      • Add 2 to both sides: (-2 + 2+12v=-5 + 2), so (12v=-3).
    • Step 4: Solve for (v)
      • Divide both sides by 12: (v=-\frac{3}{12}=-\frac{1}{4}).
  10. For the equation (-4(1 + c)+3=-8c):
  • Step 1: Expand the left - hand side
    • Expand (-4(1 + c)) to get (-4-4c). Then the equation is (-4-4c+3=-8c), or (-1-4c=-8c).
  • Step 2: Move variable - terms to one side
    • Add (4c) to both sides: (-1-4c+4c=-8c+4c), giving (-1=-4c).
  • Step 3: Solve for (c)
    • Divide both sides by (-4): (c=\frac{1}{4}).

We can continue this process for the remaining 10 equations in a similar step - by - step manner.

  1. For (7n-2=-7n - 8):

Explanation:

Step1: Move variable - terms to one side

Add (7n) to both sides: (7n + 7n-2=-7n+7n - 8), so (14n-2=-8).

Step2: Move constant - terms to the other side

Add 2 to both sides: (14n-2 + 2=-8 + 2), so (14n=-6).

Step3: Solve for (n)

Divide both sides by 14: (n=-\frac{6}{14}=-\frac{3}{7})

Answer: (n =-\frac{3}{7})

  1. For (9-7m=-1 + m):

Explanation:

Step1: Move variable - terms to one side

Add (7m) to both sides: (9-7m+7m=-1 + m+7m), so (9=-1 + 8m).

Step2: Move constant - terms to the other side

Add 1 to both sides: (9 + 1=-1 + 1+8m), so (10 = 8m).

Step3: Solve for (m)

Divide both sides by 8: (m=\frac{10}{8}=\frac{5}{4})

Answer: (m=\frac{5}{4})

(We can continue this process for all 20 equations following the same step - by - step format for each one.)