Solve -2x-1/2x-5/3y-x=4

$$- 2 x - \frac { 1 } { 2 } x - \frac { 5 } { 3 } y - x = 4$$

Solve for x

$$x=-\frac{10y}{21}-\frac{8}{7}$$

Steps for Solving Linear Equation

Combine -2x and -\frac{1}{2}x to get -\frac{5}{2}x.

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

Combine -\frac{5}{2}x and -x to get -\frac{7}{2}x.

$$-\frac{7}{2}x-\frac{5}{3}y=4$$

Add \frac{5}{3}y to both sides.

$$-\frac{7}{2}x=4+\frac{5}{3}y$$

The equation is in standard form.

$$-\frac{7}{2}x=\frac{5y}{3}+4$$

Divide both sides of the equation by -\frac{7}{2}, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{-\frac{7}{2}x}{-\frac{7}{2}}=\frac{\frac{5y}{3}+4}{-\frac{7}{2}}$$

Dividing by -\frac{7}{2} undoes the multiplication by -\frac{7}{2}.

$$x=\frac{\frac{5y}{3}+4}{-\frac{7}{2}}$$

Divide 4+\frac{5y}{3} by -\frac{7}{2} by multiplying 4+\frac{5y}{3} by the reciprocal of -\frac{7}{2}.

$$x=-\frac{10y}{21}-\frac{8}{7}$$

Solve for y

$$y=-\frac{21x}{10}-\frac{12}{5}$$

Steps for Solving Linear Equation

Combine -2x and -\frac{1}{2}x to get -\frac{5}{2}x.

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

Combine -\frac{5}{2}x and -x to get -\frac{7}{2}x.

$$-\frac{7}{2}x-\frac{5}{3}y=4$$

Add \frac{7}{2}x to both sides.

$$-\frac{5}{3}y=4+\frac{7}{2}x$$

The equation is in standard form.

$$-\frac{5}{3}y=\frac{7x}{2}+4$$

Divide both sides of the equation by -\frac{5}{3}, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{-\frac{5}{3}y}{-\frac{5}{3}}=\frac{\frac{7x}{2}+4}{-\frac{5}{3}}$$

Dividing by -\frac{5}{3} undoes the multiplication by -\frac{5}{3}.

$$y=\frac{\frac{7x}{2}+4}{-\frac{5}{3}}$$

Divide 4+\frac{7x}{2} by -\frac{5}{3} by multiplying 4+\frac{7x}{2} by the reciprocal of -\frac{5}{3}.

$$y=-\frac{21x}{10}-\frac{12}{5}$$