Solve 7-(3y+4x)=6(x-y)

$$7 - ( 3 y + 4 x ) = 6 ( x - y )$$

Solve for x

$$x=\frac{3y+7}{10}$$

Steps for Solving Linear Equation

To find the opposite of 3y+4x, find the opposite of each term.

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

Use the distributive property to multiply 6 by x-y.

$$7-3y-4x=6x-6y$$

Subtract 6x from both sides.

$$7-3y-4x-6x=-6y$$

Combine -4x and -6x to get -10x.

$$7-3y-10x=-6y$$

Subtract 7 from both sides.

$$-3y-10x=-6y-7$$

Add 3y to both sides.

$$-10x=-6y-7+3y$$

Combine -6y and 3y to get -3y.

$$-10x=-3y-7$$

Divide both sides by -10.

$$\frac{-10x}{-10}=\frac{-3y-7}{-10}$$

Dividing by -10 undoes the multiplication by -10.

$$x=\frac{-3y-7}{-10}$$

Divide -3y-7 by -10.

$$x=\frac{3y+7}{10}$$

Solve for y

$$y=\frac{10x-7}{3}$$

Steps for Solving Linear Equation

To find the opposite of 3y+4x, find the opposite of each term.

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

Use the distributive property to multiply 6 by x-y.

$$7-3y-4x=6x-6y$$

Add 6y to both sides.

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

Combine -3y and 6y to get 3y.

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

Subtract 7 from both sides.

$$3y-4x=6x-7$$

Add 4x to both sides.

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

Combine 6x and 4x to get 10x.

$$3y=10x-7$$

Divide both sides by 3.

$$\frac{3y}{3}=\frac{10x-7}{3}$$

Dividing by 3 undoes the multiplication by 3.

$$y=\frac{10x-7}{3}$$