Answer:
x=12
Step-by-step explanation:
Solve for x:
(3 (x/6 + 16))/4 = (3 ((4 + 3/8) x - 21))/7
Put 4 + 3/8 over the common denominator 8. 4 + 3/8 = (8×4)/8 + 3/8:
(3 (x/6 + 16))/4 = (3 ((8×4)/8 + 3/8 x - 21))/7
8×4 = 32:
(3 (x/6 + 16))/4 = (3 ((32/8 + 3/8) x - 21))/7
32/8 + 3/8 = (32 + 3)/8:
(3 (x/6 + 16))/4 = (3 ((32 + 3)/8 x - 21))/7
32 + 3 = 35:
(3 (x/6 + 16))/4 = (3 ((35 x)/8 - 21))/7
Put each term in x/6 + 16 over the common denominator 6: x/6 + 16 = x/6 + 96/6:
3/4 x/6 + 96/6 = (3 ((35 x)/8 - 21))/7
x/6 + 96/6 = (x + 96)/6:
3/4 (x + 96)/6 = (3 ((35 x)/8 - 21))/7
3/6 = 3/(3×2) = 1/2:
(x + 96)/(2×4) = (3 ((35 x)/8 - 21))/7
Put each term in (35 x)/8 - 21 over the common denominator 8: (35 x)/8 - 21 = (35 x)/8 - 168/8:
(x + 96)/(2×4) = 3/7 (35 x)/8 - 168/8
(35 x)/8 - 168/8 = (35 x - 168)/8:
(x + 96)/(2×4) = 3/7 (35 x - 168)/8
2×4 = 8:
(x + 96)/8 = (3 (35 x - 168))/(8×7)
8×7 = 56:
(x + 96)/8 = (3 (35 x - 168))/56
Multiply both sides by 56:
(56 (x + 96))/8 = (56×3 (35 x - 168))/56
56/8 = (8×7)/8 = 7:
7 (x + 96) = (56×3 (35 x - 168))/56
(56×3 (35 x - 168))/56 = 56/56×3 (35 x - 168) = 3 (35 x - 168):
7 (x + 96) = 3 (35 x - 168)
Expand out terms of the left hand side:
7 x + 672 = 3 (35 x - 168)
Expand out terms of the right hand side:
7 x + 672 = 105 x - 504
Subtract 105 x from both sides:
(7 x - 105 x) + 672 = (105 x - 105 x) - 504
7 x - 105 x = -98 x:
-98 x + 672 = (105 x - 105 x) - 504
105 x - 105 x = 0:
672 - 98 x = -504
Subtract 672 from both sides:
(672 - 672) - 98 x = -672 - 504
672 - 672 = 0:
-98 x = -672 - 504
-672 - 504 = -1176:
-98 x = -1176
Divide both sides of -98 x = -1176 by -98:
(-98 x)/(-98) = (-1176)/(-98)
(-98)/(-98) = 1:
x = (-1176)/(-98)
The gcd of -1176 and -98 is -98, so (-1176)/(-98) = (-98×12)/(-98×1) = (-98)/(-98)×12 = 12:
Answer: x = 12
