Solve x/3*3+x/4*4+x/6*5+(x/4-8)*2=50^4

$$\frac { x } { 3 } \times 3 + \frac { x } { 4 } \times 4 + \frac { x } { 6 } \times 5 + ( \frac { x } { 4 } - 8 ) \cdot 2 = 50 ^ { 4 }$$

Solve for x

$$x = \frac{9375024}{5} = 1875004\frac{4}{5} = 1875004.8$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 12, the least common multiple of 3,4,6.

$$4x\times 3+3x\times 4+2x\times 5+12\left(\frac{x}{4}-8\right)\times 2=12\times 50^{4}$$

Multiply 4 and 3 to get 12.

$$12x+3x\times 4+2x\times 5+12\left(\frac{x}{4}-8\right)\times 2=12\times 50^{4}$$

Multiply 3 and 4 to get 12.

$$12x+12x+2x\times 5+12\left(\frac{x}{4}-8\right)\times 2=12\times 50^{4}$$

Combine 12x and 12x to get 24x.

$$24x+2x\times 5+12\left(\frac{x}{4}-8\right)\times 2=12\times 50^{4}$$

Multiply 2 and 5 to get 10.

$$24x+10x+12\left(\frac{x}{4}-8\right)\times 2=12\times 50^{4}$$

Combine 24x and 10x to get 34x.

$$34x+12\left(\frac{x}{4}-8\right)\times 2=12\times 50^{4}$$

Multiply 12 and 2 to get 24.

$$34x+24\left(\frac{x}{4}-8\right)=12\times 50^{4}$$

Use the distributive property to multiply 24 by \frac{x}{4}-8.

$$34x+24\times \frac{x}{4}-192=12\times 50^{4}$$

Cancel out 4, the greatest common factor in 24 and 4.

$$34x+6x-192=12\times 50^{4}$$

Combine 34x and 6x to get 40x.

$$40x-192=12\times 50^{4}$$

Calculate 50 to the power of 4 and get 6250000.

$$40x-192=12\times 6250000$$

Multiply 12 and 6250000 to get 75000000.

$$40x-192=75000000$$

Add 192 to both sides.

$$40x=75000000+192$$

Add 75000000 and 192 to get 75000192.

$$40x=75000192$$

Divide both sides by 40.

$$x=\frac{75000192}{40}$$

Reduce the fraction \frac{75000192}{40} to lowest terms by extracting and canceling out 8.

$$x=\frac{9375024}{5}$$