Question

5 1/28=1/2p+5 4/7 Please help!!

Answer 1

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