Solve 2p-3/5-4-x/2=x

$$\frac { 2 p - 3 } { 5 } - \frac { 4 - x } { 2 } = x$$

Solve for p

$$p=\frac{5x}{4}+\frac{13}{2}$$

Steps for Solving Linear Equation

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 5 and 2 is 10. Multiply \frac{2p-3}{5} times \frac{2}{2}. Multiply \frac{4-x}{2} times \frac{5}{5}.

$$\frac{2\left(2p-3\right)}{10}-\frac{5\left(4-x\right)}{10}=x$$

Since \frac{2\left(2p-3\right)}{10} and \frac{5\left(4-x\right)}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2\left(2p-3\right)-5\left(4-x\right)}{10}=x$$

Do the multiplications in 2\left(2p-3\right)-5\left(4-x\right).

$$\frac{4p-6-20+5x}{10}=x$$

Combine like terms in 4p-6-20+5x.

$$\frac{4p-26+5x}{10}=x$$

Divide each term of 4p-26+5x by 10 to get \frac{2}{5}p-\frac{13}{5}+\frac{1}{2}x.

$$\frac{2}{5}p-\frac{13}{5}+\frac{1}{2}x=x$$

Add \frac{13}{5} to both sides.

$$\frac{2}{5}p+\frac{1}{2}x=x+\frac{13}{5}$$

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

$$\frac{2}{5}p=x+\frac{13}{5}-\frac{1}{2}x$$

Combine x and -\frac{1}{2}x to get \frac{1}{2}x.

$$\frac{2}{5}p=\frac{1}{2}x+\frac{13}{5}$$

The equation is in standard form.

$$\frac{2}{5}p=\frac{x}{2}+\frac{13}{5}$$

Divide both sides of the equation by \frac{2}{5}, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{\frac{2}{5}p}{\frac{2}{5}}=\frac{\frac{x}{2}+\frac{13}{5}}{\frac{2}{5}}$$

Dividing by \frac{2}{5} undoes the multiplication by \frac{2}{5}.

$$p=\frac{\frac{x}{2}+\frac{13}{5}}{\frac{2}{5}}$$

Divide \frac{x}{2}+\frac{13}{5} by \frac{2}{5} by multiplying \frac{x}{2}+\frac{13}{5} by the reciprocal of \frac{2}{5}.

$$p=\frac{5x}{4}+\frac{13}{2}$$

Solve for x

$$x=\frac{4p-26}{5}$$

Steps for Solving Linear Equation

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 5 and 2 is 10. Multiply \frac{2p-3}{5} times \frac{2}{2}. Multiply \frac{4-x}{2} times \frac{5}{5}.

$$\frac{2\left(2p-3\right)}{10}-\frac{5\left(4-x\right)}{10}=x$$

Since \frac{2\left(2p-3\right)}{10} and \frac{5\left(4-x\right)}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2\left(2p-3\right)-5\left(4-x\right)}{10}=x$$

Do the multiplications in 2\left(2p-3\right)-5\left(4-x\right).

$$\frac{4p-6-20+5x}{10}=x$$

Combine like terms in 4p-6-20+5x.

$$\frac{5x+4p-26}{10}=x$$

Divide each term of 5x+4p-26 by 10 to get \frac{1}{2}x+\frac{2}{5}p-\frac{13}{5}.

$$\frac{1}{2}x+\frac{2}{5}p-\frac{13}{5}=x$$

Subtract x from both sides.

$$\frac{1}{2}x+\frac{2}{5}p-\frac{13}{5}-x=0$$

Combine \frac{1}{2}x and -x to get -\frac{1}{2}x.

$$-\frac{1}{2}x+\frac{2}{5}p-\frac{13}{5}=0$$

Subtract \frac{2}{5}p from both sides. Anything subtracted from zero gives its negation.

$$-\frac{1}{2}x-\frac{13}{5}=-\frac{2}{5}p$$

Add \frac{13}{5} to both sides.

$$-\frac{1}{2}x=-\frac{2}{5}p+\frac{13}{5}$$

The equation is in standard form.

$$-\frac{1}{2}x=\frac{13-2p}{5}$$

Multiply both sides by -2.

$$\frac{-\frac{1}{2}x}{-\frac{1}{2}}=\frac{13-2p}{-\frac{1}{2}\times 5}$$

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

$$x=\frac{13-2p}{-\frac{1}{2}\times 5}$$

Divide \frac{-2p+13}{5} by -\frac{1}{2} by multiplying \frac{-2p+13}{5} by the reciprocal of -\frac{1}{2}.

$$x=\frac{4p-26}{5}$$