(algebra)Can you please help and show your work, solve for X.

Solve for x.

41. (x + a)/b + b = a

1. Subtract b.

(x + a)/b = a - b

2. Multiply by b.

x + a = ab - b^2

3. Subtract a.

x = ab - b^2 -a

42. bx + a = dx + c

1. Subtract a.

bx = dx + c - a

2. Subtract dx.

bx - dx = c - a

3. Factor x out.

x(b -d) = c - a

4. Divide by (b-d).

x = (c-a)/(b-d)

43. cx - b = ax + d

1. Add b.

cx = ax + d + b

2. Subtract ax.

cx - ax = d + b

3. Factor x out.

x(c -a) = d + b

4. Divide by (c-a).

x = (d +b)/c-a).

44. a(x -3) + 8 = b(x - 1)

1. Distribute everything.

ax - 3x + 8 = bx - b

2. Subtract 8.

ax - 3a = bx - b -8

3. Subtract bx.

ax - bx - 3a = -b - 8

4. Factor x out.

x ( a - b) - 3a = -b - 8

5. Add 3a.

x ( a - b) = -b - 8 + 3a

6. Divide by (a-b).

x =  (-b - 8 + 3a) / (a - b)

45. c ( x + 2) - 5 = b ( x -3)

1. Distribute everything.

cx + 2c -5 = bx - 3b

2. Add 5.

cx + 2c = bx - 3b + 5

3. Subtract bx.

cx - bx + 2c = -3b + 5

4. Factor x out.

x ( c - b ) + 2c = -3b + 5

5. Subtract 2c.

x ( c - b) = -3b + 5 - 2c

6. Divide by ( c - b).

x = (-3b + 5 - 2c)/(c-b)

46. a (3tx - 2b) = c (dx -2)

1. Distribute everything

3txa - 2ba = cdx - 2c

2. Subtract cdx.

3txa - cdx - 2ba = -2c

3. Add 2ba.

3txa - cdx = 2ba - 2c

4. Factor x out.

x ( 3ta - cd) = 2ba - 2c

5. Divide by (3ta - cd).

x = (2ba - 2c)/(3ta - cd)

47. b ( 5px - 3c) = a (qx -4)

1. Distribute everything.

5bpx - 3bc = apx - 4a

2. Subtract apx.

5bpx - apx - 3bc = -4a

3. Add 3bc.

5bpx - apx = -4a + 3bc

4. Factor x out.

x ( 5bp - ap ) = -4a + 3bc

5. Divide by (5bp - ap).

x = (-4a + 3bc)/(5bp - ap)

48. [a/b(2x - 12)]= c/d

1. Multiply b first.

a ( 2x - 12) = c/d

2. Multiply by d.

ad(2x - 12) = cb

3. Distribute ad.

2adx - 12ad = cb

4. Add 12ad.

2adx = cb + 12ad

5. Divide by 2 ad.

x = (cb + 12ad)/2ad

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