Solve 39/8+p+4/3p=3/2p-23/6

$$\frac { 39 } { 8 } + p + \frac { 4 } { 3 } p = \frac { 3 } { 2 } p - \frac { 23 } { 6 }$$

Solve for p

$$p = -\frac{209}{20} = -10\frac{9}{20} = -10.45$$

Steps for Solving Linear Equation

Combine p and \frac{4}{3}p to get \frac{7}{3}p.

$$\frac{39}{8}+\frac{7}{3}p=\frac{3}{2}p-\frac{23}{6}$$

Subtract \frac{3}{2}p from both sides.

$$\frac{39}{8}+\frac{7}{3}p-\frac{3}{2}p=-\frac{23}{6}$$

Combine \frac{7}{3}p and -\frac{3}{2}p to get \frac{5}{6}p.

$$\frac{39}{8}+\frac{5}{6}p=-\frac{23}{6}$$

Subtract \frac{39}{8} from both sides.

$$\frac{5}{6}p=-\frac{23}{6}-\frac{39}{8}$$

Least common multiple of 6 and 8 is 24. Convert -\frac{23}{6} and \frac{39}{8} to fractions with denominator 24.

$$\frac{5}{6}p=-\frac{92}{24}-\frac{117}{24}$$

Since -\frac{92}{24} and \frac{117}{24} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5}{6}p=\frac{-92-117}{24}$$

Subtract 117 from -92 to get -209.

$$\frac{5}{6}p=-\frac{209}{24}$$

Multiply both sides by \frac{6}{5}, the reciprocal of \frac{5}{6}.

$$p=-\frac{209}{24}\times \frac{6}{5}$$

Multiply -\frac{209}{24} times \frac{6}{5} by multiplying numerator times numerator and denominator times denominator.

$$p=\frac{-209\times 6}{24\times 5}$$

Do the multiplications in the fraction \frac{-209\times 6}{24\times 5}.

$$p=\frac{-1254}{120}$$

Reduce the fraction \frac{-1254}{120} to lowest terms by extracting and canceling out 6.

$$p=-\frac{209}{20}$$