Solve 2n-2(x+4)=5x+6

$$2 n - 2 ( x + 4 ) = 5 x + 6$$

Solve for n

$$n=\frac{7\left(x+2\right)}{2}$$

Steps for Solving Linear Equation

Use the distributive property to multiply -2 by x+4.

$$2n-2x-8=5x+6$$

Add 2x to both sides.

$$2n-8=5x+6+2x$$

Combine 5x and 2x to get 7x.

$$2n-8=7x+6$$

Add 8 to both sides.

$$2n=7x+6+8$$

Add 6 and 8 to get 14.

$$2n=7x+14$$

Divide both sides by 2.

$$\frac{2n}{2}=\frac{7x+14}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$n=\frac{7x+14}{2}$$

Divide 14+7x by 2.

$$n=\frac{7x}{2}+7$$

Solve for x

$$x=\frac{2\left(n-7\right)}{7}$$

Steps for Solving Linear Equation

Use the distributive property to multiply -2 by x+4.

$$2n-2x-8=5x+6$$

Subtract 5x from both sides.

$$2n-2x-8-5x=6$$

Combine -2x and -5x to get -7x.

$$2n-7x-8=6$$

Subtract 2n from both sides.

$$-7x-8=6-2n$$

Add 8 to both sides.

$$-7x=6-2n+8$$

Add 6 and 8 to get 14.

$$-7x=14-2n$$

Divide both sides by -7.

$$\frac{-7x}{-7}=\frac{14-2n}{-7}$$

Dividing by -7 undoes the multiplication by -7.

$$x=\frac{14-2n}{-7}$$

Divide 14-2n by -7.

$$x=\frac{2n}{7}-2$$