Question

Select the correct answer.

What is the solution for p in the equation?

1/3p + 1/2p = 7/6p +5 + 4

A.
p = -6
B.
p = -1
C.
p = 1
D.
p = 6

Answer 1

To solve for p in the equation 1/3p + 1/2p = 7/6p + 5 + 4, you need to combine like terms and isolate p. The solution is p = 27.

Step-by-step explanation:

To solve for p in the equation 1/3p + 1/2p = 7/6p + 5 + 4, you need to combine like terms and isolate p on one side of the equation.

Multiply the fractions by their respective denominators to eliminate the fractions. This gives us 2/6p + 3/6p = 7/6p + 9.

Combine like terms. On the left side, 2/6p + 3/6p = 5/6p. On the right side, 7/6p + 9 remains unchanged.

Subtract 5/6p from both sides to isolate p. This gives us 7/6p - 5/6p = 9.

Combine like terms on the left side. 7/6p - 5/6p = 2/6p.

Simplify the equation further. 2/6p = 9 can be reduced to 1/3p = 9.

Multiply both sides of the equation by the reciprocal of 1/3, which is 3/1. This gives us p = 9 * (3/1) = 27.

Therefore, the solution for p in the equation is p = 27.

Answer 2

Step-by-step explanation:

Problems such as this one become easier to solve if we first eliminate fractions. Here the LCD is 6 (which is 2 times 3).

Multiplying all 5 terms by 6, we get:

2p + 3p = 7p + 54, or

5p = 7p + 54. Then,

-2p = 54, or p = -27

Double check to ensure that you have copied down the last two terms (5 and 4) correctly.