Answer:
p = (-15)/14
Step-by-step explanation:
Solve for p:
5 + 1/28 = p/2 + 4/7 + 5
Put 5 + 1/28 over the common denominator 28. 5 + 1/28 = (28×5)/28 + 1/28:
((28×5)/28 + 1/28) = p/2 + 4/7 + 5
28×5 = 140:
140/28 + 1/28 = p/2 + 4/7 + 5
140/28 + 1/28 = (140 + 1)/28:
((140 + 1)/28) = p/2 + 4/7 + 5
140 + 1 = 141:
141/28 = p/2 + 4/7 + 5
Put each term in p/2 + 4/7 + 5 over the common denominator 14: p/2 + 4/7 + 5 = (7 p)/14 + 8/14 + 70/14:
141/28 = ((7 p)/14 + 8/14 + 70/14)
(7 p)/14 + 8/14 + 70/14 = (7 p + 8 + 70)/14:
141/28 = ((7 p + 8 + 70)/14)
Grouping like terms, 7 p + 8 + 70 = 7 p + (70 + 8):
141/28 = (7 p + (70 + 8))/14
70 + 8 = 78:
141/28 = (7 p + 78)/14
141/28 = (7 p + 78)/14 is equivalent to (7 p + 78)/14 = 141/28:
(7 p + 78)/14 = 141/28
Multiply both sides of (7 p + 78)/14 = 141/28 by 14:
(14 (7 p + 78))/14 = (14×141)/28
(14 (7 p + 78))/14 = 14/14×(7 p + 78) = 7 p + 78:
(7 p + 78) = (14×141)/28
14/28 = 14/(14×2) = 1/2:
7 p + 78 = 141/2
Subtract 78 from both sides:
7 p + (78 - 78) = 141/2 - 78
78 - 78 = 0:
7 p = 141/2 - 78
Put 141/2 - 78 over the common denominator 2. 141/2 - 78 = 141/2 + (2 (-78))/2:
7 p = (141/2 - (78×2)/2)
2 (-78) = -156:
7 p = 141/2 + (-156)/2
141/2 - 156/2 = (141 - 156)/2:
7 p = ((141 - 156)/2)
141 - 156 = -15:
7 p = (-15)/2
Divide both sides by 7:
p = ((-15)/7)/2
2×7 = 14:
Answer: p = (-15)/14
