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