Solve 4z-(2x-6)=7+(-4z-2)+5

$$4 z - ( 2 x - 6 ) = 7 + ( - 4 z - 2 ) + 5$$

Solve for x

$$x=4z-2$$

Steps for Solving Linear Equation

To find the opposite of 2x-6, find the opposite of each term.

$$4z-2x+6=7-4z-2+5$$

Subtract 2 from 7 to get 5.

$$4z-2x+6=5-4z+5$$

Add 5 and 5 to get 10.

$$4z-2x+6=10-4z$$

Subtract 4z from both sides.

$$-2x+6=10-4z-4z$$

Combine -4z and -4z to get -8z.

$$-2x+6=10-8z$$

Subtract 6 from both sides.

$$-2x=10-8z-6$$

Subtract 6 from 10 to get 4.

$$-2x=4-8z$$

Divide both sides by -2.

$$\frac{-2x}{-2}=\frac{4-8z}{-2}$$

Dividing by -2 undoes the multiplication by -2.

$$x=\frac{4-8z}{-2}$$

Divide 4-8z by -2.

$$x=4z-2$$

Solve for z

$$z=\frac{x+2}{4}$$

Steps for Solving Linear Equation

To find the opposite of 2x-6, find the opposite of each term.

$$4z-2x+6=7-4z-2+5$$

Subtract 2 from 7 to get 5.

$$4z-2x+6=5-4z+5$$

Add 5 and 5 to get 10.

$$4z-2x+6=10-4z$$

Add 4z to both sides.

$$4z-2x+6+4z=10$$

Combine 4z and 4z to get 8z.

$$8z-2x+6=10$$

Add 2x to both sides.

$$8z+6=10+2x$$

Subtract 6 from both sides.

$$8z=10+2x-6$$

Subtract 6 from 10 to get 4.

$$8z=4+2x$$

The equation is in standard form.

$$8z=2x+4$$

Divide both sides by 8.

$$\frac{8z}{8}=\frac{2x+4}{8}$$

Dividing by 8 undoes the multiplication by 8.

$$z=\frac{2x+4}{8}$$

Divide 4+2x by 8.

$$z=\frac{x}{4}+\frac{1}{2}$$