Solve 3600left(x-2right)+4200x/4200x-3600left(x-2right)=1500/300

$$\frac{ 3600 \left( x-2 \right) +4200x }{ 4200x-3600 \left( x-2 \right) } = \frac{ 1500 }{ 300 }$$

Solve for x

$$x=9$$

Steps for Solving Linear Equation

Variable x cannot be equal to -12 since division by zero is not defined. Multiply both sides of the equation by 600\left(x+12\right), the least common multiple of 4200x-3600\left(x-2\right),300.

$$3600\left(x-2\right)+4200x=\left(2x+24\right)\times 1500$$

Use the distributive property to multiply 3600 by x-2.

$$3600x-7200+4200x=\left(2x+24\right)\times 1500$$

Combine 3600x and 4200x to get 7800x.

$$7800x-7200=\left(2x+24\right)\times 1500$$

Use the distributive property to multiply 2x+24 by 1500.

$$7800x-7200=3000x+36000$$

Subtract 3000x from both sides.

$$7800x-7200-3000x=36000$$

Combine 7800x and -3000x to get 4800x.

$$4800x-7200=36000$$

Add 7200 to both sides.

$$4800x=36000+7200$$

Add 36000 and 7200 to get 43200.

$$4800x=43200$$

Divide both sides by 4800.

$$x=\frac{43200}{4800}$$

Divide 43200 by 4800 to get 9.

$$x=9$$