Solve 10/r-3x+5/6=3/12-frac{x/2}{4}

$$\frac { 10 } { r } - \frac { 3 x + 5 } { 6 } = \frac { 3 } { 12 } - \frac { \frac { x } { 2 } } { 4 }$$

Solve for r

$$r=\frac{240}{9x+26}$$

$$x\neq -\frac{26}{9}$$

Steps for Solving Linear Equation

Variable r cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 12r, the least common multiple of r,6,12,4.

$$12\times 10-2r\left(3x+5\right)=r\times 3-3r\times \frac{x}{2}$$

Multiply 12 and 10 to get 120.

$$120-2r\left(3x+5\right)=r\times 3-3r\times \frac{x}{2}$$

Use the distributive property to multiply 2r by 3x+5.

$$120-\left(6rx+10r\right)=r\times 3-3r\times \frac{x}{2}$$

To find the opposite of 6rx+10r, find the opposite of each term.

$$120-6rx-10r=r\times 3-3r\times \frac{x}{2}$$

Express 3\times \frac{x}{2} as a single fraction.

$$120-6rx-10r=r\times 3-\frac{3x}{2}r$$

Express \frac{3x}{2}r as a single fraction.

$$120-6rx-10r=r\times 3-\frac{3xr}{2}$$

Subtract r\times 3 from both sides.

$$120-6rx-10r-r\times 3=-\frac{3xr}{2}$$

Combine -10r and -r\times 3 to get -13r.

$$120-6rx-13r=-\frac{3xr}{2}$$

Add \frac{3xr}{2} to both sides.

$$120-6rx-13r+\frac{3xr}{2}=0$$

Subtract 120 from both sides. Anything subtracted from zero gives its negation.

$$-6rx-13r+\frac{3xr}{2}=-120$$

Multiply both sides of the equation by 2.

$$-12rx-26r+3xr=-240$$

Combine -12rx and 3xr to get -9rx.

$$-9rx-26r=-240$$

Combine all terms containing r.

$$\left(-9x-26\right)r=-240$$

Divide both sides by -9x-26.

$$\frac{\left(-9x-26\right)r}{-9x-26}=-\frac{240}{-9x-26}$$

Dividing by -9x-26 undoes the multiplication by -9x-26.

$$r=-\frac{240}{-9x-26}$$

Divide -240 by -9x-26.

$$r=\frac{240}{9x+26}$$

Variable r cannot be equal to 0.

$$r=\frac{240}{9x+26}\text{, }r\neq 0$$

Solve for x

$$x=-\frac{26}{9}+\frac{80}{3r}$$

$$r\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 12r, the least common multiple of r,6,12,4.

$$12\times 10-2r\left(3x+5\right)=r\times 3-3r\times \frac{x}{2}$$

Multiply 12 and 10 to get 120.

$$120-2r\left(3x+5\right)=r\times 3-3r\times \frac{x}{2}$$

Use the distributive property to multiply 2r by 3x+5.

$$120-\left(6xr+10r\right)=r\times 3-3r\times \frac{x}{2}$$

To find the opposite of 6xr+10r, find the opposite of each term.

$$120-6xr-10r=r\times 3-3r\times \frac{x}{2}$$

Express 3\times \frac{x}{2} as a single fraction.

$$120-6xr-10r=r\times 3-\frac{3x}{2}r$$

Express \frac{3x}{2}r as a single fraction.

$$120-6xr-10r=r\times 3-\frac{3xr}{2}$$

Add \frac{3xr}{2} to both sides.

$$120-6xr-10r+\frac{3xr}{2}=r\times 3$$

Subtract 120 from both sides.

$$-6xr-10r+\frac{3xr}{2}=r\times 3-120$$

Add 10r to both sides.

$$-6xr+\frac{3xr}{2}=r\times 3-120+10r$$

Combine r\times 3 and 10r to get 13r.

$$-6xr+\frac{3xr}{2}=13r-120$$

Multiply both sides of the equation by 2.

$$-12xr+3xr=26r-240$$

Combine -12xr and 3xr to get -9xr.

$$-9xr=26r-240$$

The equation is in standard form.

$$\left(-9r\right)x=26r-240$$

Divide both sides by -9r.

$$\frac{\left(-9r\right)x}{-9r}=\frac{26r-240}{-9r}$$

Dividing by -9r undoes the multiplication by -9r.

$$x=\frac{26r-240}{-9r}$$

Divide 26r-240 by -9r.

$$x=-\frac{26}{9}+\frac{80}{3r}$$