Solve 5x+m/3-x-1/2=m

$$\frac { 5 x + m } { 3 } - \frac { x - 1 } { 2 } = m$$

Solve for m

$$m=\frac{7x+3}{4}$$

Steps for Solving Linear Equation

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3 and 2 is 6. Multiply \frac{5x+m}{3} times \frac{2}{2}. Multiply \frac{x-1}{2} times \frac{3}{3}.

$$\frac{2\left(5x+m\right)}{6}-\frac{3\left(x-1\right)}{6}=m$$

Since \frac{2\left(5x+m\right)}{6} and \frac{3\left(x-1\right)}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2\left(5x+m\right)-3\left(x-1\right)}{6}=m$$

Do the multiplications in 2\left(5x+m\right)-3\left(x-1\right).

$$\frac{10x+2m-3x+3}{6}=m$$

Combine like terms in 10x+2m-3x+3.

$$\frac{2m+7x+3}{6}=m$$

Divide each term of 2m+7x+3 by 6 to get \frac{1}{3}m+\frac{7}{6}x+\frac{1}{2}.

$$\frac{1}{3}m+\frac{7}{6}x+\frac{1}{2}=m$$

Subtract m from both sides.

$$\frac{1}{3}m+\frac{7}{6}x+\frac{1}{2}-m=0$$

Combine \frac{1}{3}m and -m to get -\frac{2}{3}m.

$$-\frac{2}{3}m+\frac{7}{6}x+\frac{1}{2}=0$$

Subtract \frac{7}{6}x from both sides. Anything subtracted from zero gives its negation.

$$-\frac{2}{3}m+\frac{1}{2}=-\frac{7}{6}x$$

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

$$-\frac{2}{3}m=-\frac{7}{6}x-\frac{1}{2}$$

The equation is in standard form.

$$-\frac{2}{3}m=-\frac{7x}{6}-\frac{1}{2}$$

Divide both sides of the equation by -\frac{2}{3}, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{-\frac{2}{3}m}{-\frac{2}{3}}=\frac{-\frac{7x}{6}-\frac{1}{2}}{-\frac{2}{3}}$$

Dividing by -\frac{2}{3} undoes the multiplication by -\frac{2}{3}.

$$m=\frac{-\frac{7x}{6}-\frac{1}{2}}{-\frac{2}{3}}$$

Divide -\frac{7x}{6}-\frac{1}{2} by -\frac{2}{3} by multiplying -\frac{7x}{6}-\frac{1}{2} by the reciprocal of -\frac{2}{3}.

$$m=\frac{7x+3}{4}$$

Solve for x

$$x=\frac{4m-3}{7}$$

Steps for Solving Linear Equation

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3 and 2 is 6. Multiply \frac{5x+m}{3} times \frac{2}{2}. Multiply \frac{x-1}{2} times \frac{3}{3}.

$$\frac{2\left(5x+m\right)}{6}-\frac{3\left(x-1\right)}{6}=m$$

Since \frac{2\left(5x+m\right)}{6} and \frac{3\left(x-1\right)}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2\left(5x+m\right)-3\left(x-1\right)}{6}=m$$

Do the multiplications in 2\left(5x+m\right)-3\left(x-1\right).

$$\frac{10x+2m-3x+3}{6}=m$$

Combine like terms in 10x+2m-3x+3.

$$\frac{7x+2m+3}{6}=m$$

Divide each term of 7x+2m+3 by 6 to get \frac{7}{6}x+\frac{1}{3}m+\frac{1}{2}.

$$\frac{7}{6}x+\frac{1}{3}m+\frac{1}{2}=m$$

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

$$\frac{7}{6}x+\frac{1}{2}=m-\frac{1}{3}m$$

Combine m and -\frac{1}{3}m to get \frac{2}{3}m.

$$\frac{7}{6}x+\frac{1}{2}=\frac{2}{3}m$$

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

$$\frac{7}{6}x=\frac{2}{3}m-\frac{1}{2}$$

The equation is in standard form.

$$\frac{7}{6}x=\frac{2m}{3}-\frac{1}{2}$$

Divide both sides of the equation by \frac{7}{6}, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{\frac{7}{6}x}{\frac{7}{6}}=\frac{\frac{2m}{3}-\frac{1}{2}}{\frac{7}{6}}$$

Dividing by \frac{7}{6} undoes the multiplication by \frac{7}{6}.

$$x=\frac{\frac{2m}{3}-\frac{1}{2}}{\frac{7}{6}}$$

Divide \frac{2m}{3}-\frac{1}{2} by \frac{7}{6} by multiplying \frac{2m}{3}-\frac{1}{2} by the reciprocal of \frac{7}{6}.

$$x=\frac{4m-3}{7}$$