determine the value of the unknown in each equation.\n1. 4(r - 2)=-2(4r - 3)\n2. 2(-4 - w)-5w = 1\n3. 9 - 2q…

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

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

Answer

  1. For the equation (4(r - 2)=-2(4r - 3)):
    • Step 1: Expand both sides
      • Expand the left - hand side: (4(r - 2)=4r-8) using the distributive property (a(b - c)=ab - ac) where (a = 4), (b=r), and (c = 2).
      • Expand the right - hand side: (-2(4r - 3)=-8r + 6) using the distributive property (a(b - c)=ab - ac) where (a=-2), (b = 4r), and (c = 3).
      • So the equation becomes (4r-8=-8r + 6).
    • Step 2: Add (8r) to both sides
      • (4r+8r-8=-8r+8r + 6), which simplifies to (12r-8 = 6).
    • Step 3: Add 8 to both sides
      • (12r-8 + 8=6 + 8), resulting in (12r=14).
    • Step 4: Divide both sides by 12
      • (r=\frac{14}{12}=\frac{7}{6}).
  2. For the equation (2(-4 - w)-5w = 1):
    • Step 1: Expand the left - hand side
      • (2(-4 - w)=-8-2w) using the distributive property (a(b + c)=ab+ac) where (a = 2), (b=-4), and (c=-w).
      • The equation is (-8-2w-5w = 1).
    • Step 2: Combine like terms on the left - hand side
      • (-8-(2w + 5w)=1), so (-8-7w = 1).
    • Step 3: Add 8 to both sides
      • (-7w=1 + 8=9).
    • Step 4: Divide both sides by (-7)
      • (w=-\frac{9}{7}).
  3. For the equation (9-2q=6 + 9q):
    • Step 1: Add (2q) to both sides
      • (9-2q+2q=6 + 9q+2q), which gives (9=6 + 11q).
    • Step 2: Subtract 6 from both sides
      • (9-6=11q), so (3 = 11q).
    • Step 3: Divide both sides by 11
      • (q=\frac{3}{11}).

We can follow the same steps (expand, combine like terms, isolate the variable) for the remaining equations.

For example, for the last equation (5x+3=7 + 8x):

  • Step 1: Subtract (5x) from both sides
    • (5x-5x+3=7 + 8x-5x), resulting in (3=7 + 3x).
  • Step 2: Subtract 7 from both sides
    • (3-7=3x), so (-4 = 3x).
  • Step 3: Divide both sides by 3
    • (x=-\frac{4}{3}).

If you want all the solutions:

  1. (r=\frac{7}{6})
  2. (w=-\frac{9}{7})
  3. (q=\frac{3}{11})
  4. (v=-\frac{3}{11})
  5. (y=-\frac{2}{15})
  6. (k=\frac{7}{12})
  7. (s=3)
  8. (a=\frac{2}{3})
  9. (c = 2)
  10. (n=-3)
  11. (g=-2)
  12. (t=3)
  13. (b = 0)
  14. (h=-\frac{3}{11})
  15. (d=-\frac{13}{6})
  16. (j=-13)
  17. (m=\frac{7}{2})
  18. (z=-\frac{6}{13})
  19. (p=\frac{8}{3})
  20. (x=-\frac{4}{3})