Solve y(7-x)-3(x-2)=4(x-3)

$$y ( 7 - x ) - 3 ( x - 2 ) = 4 ( x - 3 )$$

Solve for x

$$x=\frac{7y+18}{y+7}$$

$$y\neq -7$$

Steps for Solving Linear Equation

Use the distributive property to multiply y by 7-x.

$$7y-yx-3\left(x-2\right)=4\left(x-3\right)$$

Use the distributive property to multiply -3 by x-2.

$$7y-yx-3x+6=4\left(x-3\right)$$

Use the distributive property to multiply 4 by x-3.

$$7y-yx-3x+6=4x-12$$

Subtract 4x from both sides.

$$7y-yx-3x+6-4x=-12$$

Combine -3x and -4x to get -7x.

$$7y-yx-7x+6=-12$$

Subtract 7y from both sides.

$$-yx-7x+6=-12-7y$$

Subtract 6 from both sides.

$$-yx-7x=-12-7y-6$$

Subtract 6 from -12 to get -18.

$$-yx-7x=-18-7y$$

Combine all terms containing x.

$$\left(-y-7\right)x=-18-7y$$

The equation is in standard form.

$$\left(-y-7\right)x=-7y-18$$

Divide both sides by -y-7.

$$\frac{\left(-y-7\right)x}{-y-7}=\frac{-7y-18}{-y-7}$$

Dividing by -y-7 undoes the multiplication by -y-7.

$$x=\frac{-7y-18}{-y-7}$$

Divide -18-7y by -y-7.

$$x=\frac{7y+18}{y+7}$$

Solve for y

$$y=-\frac{18-7x}{7-x}$$

$$x\neq 7$$

Steps for Solving Linear Equation

Use the distributive property to multiply y by 7-x.

$$7y-yx-3\left(x-2\right)=4\left(x-3\right)$$

Use the distributive property to multiply -3 by x-2.

$$7y-yx-3x+6=4\left(x-3\right)$$

Use the distributive property to multiply 4 by x-3.

$$7y-yx-3x+6=4x-12$$

Add 3x to both sides.

$$7y-yx+6=4x-12+3x$$

Combine 4x and 3x to get 7x.

$$7y-yx+6=7x-12$$

Subtract 6 from both sides.

$$7y-yx=7x-12-6$$

Subtract 6 from -12 to get -18.

$$7y-yx=7x-18$$

Combine all terms containing y.

$$\left(7-x\right)y=7x-18$$

Divide both sides by 7-x.

$$\frac{\left(7-x\right)y}{7-x}=\frac{7x-18}{7-x}$$

Dividing by 7-x undoes the multiplication by 7-x.

$$y=\frac{7x-18}{7-x}$$