Solve x+4/2-6+r/4=1/10

$$\frac { x + 4 } { 2 } - \frac { 6 + r } { 4 } = \frac { 1 } { 10 }$$

Solve for r

$$r=2x+\frac{8}{5}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 20, the least common multiple of 2,4,10.

$$10\left(x+4\right)-5\left(6+r\right)=2$$

Use the distributive property to multiply 10 by x+4.

$$10x+40-5\left(6+r\right)=2$$

Use the distributive property to multiply -5 by 6+r.

$$10x+40-30-5r=2$$

Subtract 30 from 40 to get 10.

$$10x+10-5r=2$$

Subtract 10x from both sides.

$$10-5r=2-10x$$

Subtract 10 from both sides.

$$-5r=2-10x-10$$

Subtract 10 from 2 to get -8.

$$-5r=-8-10x$$

The equation is in standard form.

$$-5r=-10x-8$$

Divide both sides by -5.

$$\frac{-5r}{-5}=\frac{-10x-8}{-5}$$

Dividing by -5 undoes the multiplication by -5.

$$r=\frac{-10x-8}{-5}$$

Divide -8-10x by -5.

$$r=2x+\frac{8}{5}$$

Solve for x

$$x=\frac{r}{2}-\frac{4}{5}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 20, the least common multiple of 2,4,10.

$$10\left(x+4\right)-5\left(6+r\right)=2$$

Use the distributive property to multiply 10 by x+4.

$$10x+40-5\left(6+r\right)=2$$

Use the distributive property to multiply -5 by 6+r.

$$10x+40-30-5r=2$$

Subtract 30 from 40 to get 10.

$$10x+10-5r=2$$

Subtract 10 from both sides.

$$10x-5r=2-10$$

Subtract 10 from 2 to get -8.

$$10x-5r=-8$$

Add 5r to both sides.

$$10x=-8+5r$$

The equation is in standard form.

$$10x=5r-8$$

Divide both sides by 10.

$$\frac{10x}{10}=\frac{5r-8}{10}$$

Dividing by 10 undoes the multiplication by 10.

$$x=\frac{5r-8}{10}$$

Divide -8+5r by 10.

$$x=\frac{r}{2}-\frac{4}{5}$$