Solve -94=-2(-32/3p+1)+41/6p

$$- 94 = - 2 ( - 3 \frac { 2 } { 3 } p + 1 ) + 4 \frac { 1 } { 6 } p$$

Solve for p

$$p=-8$$

Steps for Solving Linear Equation

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

$$-564=-12\left(\left(-\frac{3\times 3+2}{3}\right)p+1\right)+\left(4\times 6+1\right)p$$

Multiply 3 and 3 to get 9.

$$-564=-12\left(\left(-\frac{9+2}{3}\right)p+1\right)+\left(4\times 6+1\right)p$$

Add 9 and 2 to get 11.

$$-564=-12\left(-\frac{11}{3}p+1\right)+\left(4\times 6+1\right)p$$

Use the distributive property to multiply -12 by -\frac{11}{3}p+1.

$$-564=-12\left(-\frac{11}{3}\right)p-12+\left(4\times 6+1\right)p$$

Express -12\left(-\frac{11}{3}\right) as a single fraction.

$$-564=\frac{-12\left(-11\right)}{3}p-12+\left(4\times 6+1\right)p$$

Multiply -12 and -11 to get 132.

$$-564=\frac{132}{3}p-12+\left(4\times 6+1\right)p$$

Divide 132 by 3 to get 44.

$$-564=44p-12+\left(4\times 6+1\right)p$$

Multiply 4 and 6 to get 24.

$$-564=44p-12+\left(24+1\right)p$$

Add 24 and 1 to get 25.

$$-564=44p-12+25p$$

Combine 44p and 25p to get 69p.

$$-564=69p-12$$

Swap sides so that all variable terms are on the left hand side.

$$69p-12=-564$$

Add 12 to both sides.

$$69p=-564+12$$

Add -564 and 12 to get -552.

$$69p=-552$$

Divide both sides by 69.

$$p=\frac{-552}{69}$$

Divide -552 by 69 to get -8.

$$p=-8$$