Solve 1-p/6+2p/3-1-7p/4=21/6

$$\frac { 1 - p } { 6 } + \frac { 2 p } { 3 } - \frac { 1 - 7 p } { 4 } = 2 \frac { 1 } { 6 }$$

Solve for p

$$p=1$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 12, the least common multiple of 6,3,4.

$$2\left(1-p\right)+4\times 2p-3\left(1-7p\right)=2\left(2\times 6+1\right)$$

Use the distributive property to multiply 2 by 1-p.

$$2-2p+4\times 2p-3\left(1-7p\right)=2\left(2\times 6+1\right)$$

Multiply 4 and 2 to get 8.

$$2-2p+8p-3\left(1-7p\right)=2\left(2\times 6+1\right)$$

Combine -2p and 8p to get 6p.

$$2+6p-3\left(1-7p\right)=2\left(2\times 6+1\right)$$

Use the distributive property to multiply -3 by 1-7p.

$$2+6p-3+21p=2\left(2\times 6+1\right)$$

Subtract 3 from 2 to get -1.

$$-1+6p+21p=2\left(2\times 6+1\right)$$

Combine 6p and 21p to get 27p.

$$-1+27p=2\left(2\times 6+1\right)$$

Multiply 2 and 6 to get 12.

$$-1+27p=2\left(12+1\right)$$

Add 12 and 1 to get 13.

$$-1+27p=2\times 13$$

Multiply 2 and 13 to get 26.

$$-1+27p=26$$

Add 1 to both sides.

$$27p=26+1$$

Add 26 and 1 to get 27.

$$27p=27$$

Divide both sides by 27.

$$p=\frac{27}{27}$$

Divide 27 by 27 to get 1.

$$p=1$$