Solve 5(x+1)/7-2(y+2)/3=-2

$$\frac { 5 ( x + 1 ) } { 7 } - \frac { 2 ( y + 2 ) } { 3 } = - 2$$

Solve for x

$$x=\frac{14y-29}{15}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 21, the least common multiple of 7,3.

$$3\times 5\left(x+1\right)-7\times 2\left(y+2\right)=-42$$

Multiply 3 and 5 to get 15.

$$15\left(x+1\right)-7\times 2\left(y+2\right)=-42$$

Use the distributive property to multiply 15 by x+1.

$$15x+15-7\times 2\left(y+2\right)=-42$$

Multiply -7 and 2 to get -14.

$$15x+15-14\left(y+2\right)=-42$$

Use the distributive property to multiply -14 by y+2.

$$15x+15-14y-28=-42$$

Subtract 28 from 15 to get -13.

$$15x-13-14y=-42$$

Add 13 to both sides.

$$15x-14y=-42+13$$

Add -42 and 13 to get -29.

$$15x-14y=-29$$

Add 14y to both sides.

$$15x=-29+14y$$

The equation is in standard form.

$$15x=14y-29$$

Divide both sides by 15.

$$\frac{15x}{15}=\frac{14y-29}{15}$$

Dividing by 15 undoes the multiplication by 15.

$$x=\frac{14y-29}{15}$$

Solve for y

$$y=\frac{15x+29}{14}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 21, the least common multiple of 7,3.

$$3\times 5\left(x+1\right)-7\times 2\left(y+2\right)=-42$$

Multiply 3 and 5 to get 15.

$$15\left(x+1\right)-7\times 2\left(y+2\right)=-42$$

Use the distributive property to multiply 15 by x+1.

$$15x+15-7\times 2\left(y+2\right)=-42$$

Multiply -7 and 2 to get -14.

$$15x+15-14\left(y+2\right)=-42$$

Use the distributive property to multiply -14 by y+2.

$$15x+15-14y-28=-42$$

Subtract 28 from 15 to get -13.

$$15x-13-14y=-42$$

Subtract 15x from both sides.

$$-13-14y=-42-15x$$

Add 13 to both sides.

$$-14y=-42-15x+13$$

Add -42 and 13 to get -29.

$$-14y=-29-15x$$

The equation is in standard form.

$$-14y=-15x-29$$

Divide both sides by -14.

$$\frac{-14y}{-14}=\frac{-15x-29}{-14}$$

Dividing by -14 undoes the multiplication by -14.

$$y=\frac{-15x-29}{-14}$$

Divide -29-15x by -14.

$$y=\frac{15x+29}{14}$$