Solve x/c+x/4-10=x/3+8

$$\frac { x } { c } + \frac { x } { 4 } - 10 = \frac { x } { 3 } + 8$$

Solve for c

$$c=\frac{12x}{x+216}$$

$$x\neq 0\text{ and }x\neq -216$$

Steps for Solving Linear Equation

Variable c cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 12c, the least common multiple of c,4,3.

$$12x+3cx+12c\left(-10\right)=4cx+12c\times 8$$

Multiply 12 and -10 to get -120.

$$12x+3cx-120c=4cx+12c\times 8$$

Multiply 12 and 8 to get 96.

$$12x+3cx-120c=4cx+96c$$

Subtract 4cx from both sides.

$$12x+3cx-120c-4cx=96c$$

Combine 3cx and -4cx to get -cx.

$$12x-cx-120c=96c$$

Subtract 96c from both sides.

$$12x-cx-120c-96c=0$$

Combine -120c and -96c to get -216c.

$$12x-cx-216c=0$$

Subtract 12x from both sides. Anything subtracted from zero gives its negation.

$$-cx-216c=-12x$$

Combine all terms containing c.

$$\left(-x-216\right)c=-12x$$

Divide both sides by -x-216.

$$\frac{\left(-x-216\right)c}{-x-216}=-\frac{12x}{-x-216}$$

Dividing by -x-216 undoes the multiplication by -x-216.

$$c=-\frac{12x}{-x-216}$$

Divide -12x by -x-216.

$$c=\frac{12x}{x+216}$$

Variable c cannot be equal to 0.

$$c=\frac{12x}{x+216}\text{, }c\neq 0$$

Solve for x

$$x=\frac{216c}{12-c}$$

$$c\neq 12\text{ and }c\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 12c, the least common multiple of c,4,3.

$$12x+3cx+12c\left(-10\right)=4cx+12c\times 8$$

Multiply 12 and -10 to get -120.

$$12x+3cx-120c=4cx+12c\times 8$$

Multiply 12 and 8 to get 96.

$$12x+3cx-120c=4cx+96c$$

Subtract 4cx from both sides.

$$12x+3cx-120c-4cx=96c$$

Combine 3cx and -4cx to get -cx.

$$12x-cx-120c=96c$$

Add 120c to both sides.

$$12x-cx=96c+120c$$

Combine 96c and 120c to get 216c.

$$12x-cx=216c$$

Combine all terms containing x.

$$\left(12-c\right)x=216c$$

Divide both sides by -c+12.

$$\frac{\left(12-c\right)x}{12-c}=\frac{216c}{12-c}$$

Dividing by -c+12 undoes the multiplication by -c+12.

$$x=\frac{216c}{12-c}$$