Solve 1/2p+1/3q+1/4r=s

$$\frac{ 1 }{ 2 } p+ \frac{ 1 }{ 3 } q+ \frac{ 1 }{ 4 } r = s$$

Solve for p

$$p=-\frac{r}{2}-\frac{2q}{3}+2s$$

Steps for Solving Linear Equation

Subtract \frac{1}{3}q from both sides.

$$\frac{1}{2}p+\frac{1}{4}r=s-\frac{1}{3}q$$

Subtract \frac{1}{4}r from both sides.

$$\frac{1}{2}p=s-\frac{1}{3}q-\frac{1}{4}r$$

The equation is in standard form.

$$\frac{1}{2}p=-\frac{q}{3}-\frac{r}{4}+s$$

Multiply both sides by 2.

$$\frac{\frac{1}{2}p}{\frac{1}{2}}=\frac{-\frac{q}{3}-\frac{r}{4}+s}{\frac{1}{2}}$$

Dividing by \frac{1}{2} undoes the multiplication by \frac{1}{2}.

$$p=\frac{-\frac{q}{3}-\frac{r}{4}+s}{\frac{1}{2}}$$

Divide s-\frac{q}{3}-\frac{r}{4} by \frac{1}{2} by multiplying s-\frac{q}{3}-\frac{r}{4} by the reciprocal of \frac{1}{2}.

$$p=-\frac{r}{2}-\frac{2q}{3}+2s$$

Solve for q

$$q=-\frac{3p}{2}-\frac{3r}{4}+3s$$

Steps for Solving Linear Equation

Subtract \frac{1}{2}p from both sides.

$$\frac{1}{3}q+\frac{1}{4}r=s-\frac{1}{2}p$$

Subtract \frac{1}{4}r from both sides.

$$\frac{1}{3}q=s-\frac{1}{2}p-\frac{1}{4}r$$

The equation is in standard form.

$$\frac{1}{3}q=-\frac{p}{2}-\frac{r}{4}+s$$

Multiply both sides by 3.

$$\frac{\frac{1}{3}q}{\frac{1}{3}}=\frac{-\frac{p}{2}-\frac{r}{4}+s}{\frac{1}{3}}$$

Dividing by \frac{1}{3} undoes the multiplication by \frac{1}{3}.

$$q=\frac{-\frac{p}{2}-\frac{r}{4}+s}{\frac{1}{3}}$$

Divide s-\frac{p}{2}-\frac{r}{4} by \frac{1}{3} by multiplying s-\frac{p}{2}-\frac{r}{4} by the reciprocal of \frac{1}{3}.

$$q=-\frac{3p}{2}-\frac{3r}{4}+3s$$