Solve 1/3*3+x/4*4+x/6*5+(x/4-8)*2=504

$$\frac { 1 } { 3 } \cdot 3 + \frac { x } { 4 } \cdot 4 + \frac { x } { 6 } \cdot 5 + ( \frac { x } { 4 } - 8 ) \cdot 2 = 504$$

Solve for x

$$x = \frac{1557}{7} = 222\frac{3}{7} \approx 222.428571429$$

Steps for Solving Linear Equation

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

$$4\times 3+3x\times 4+2x\times 5+12\left(\frac{x}{4}-8\right)\times 2=6048$$

Multiply 4 and 3 to get 12.

$$12+3x\times 4+2x\times 5+12\left(\frac{x}{4}-8\right)\times 2=6048$$

Multiply 3 and 4 to get 12.

$$12+12x+2x\times 5+12\left(\frac{x}{4}-8\right)\times 2=6048$$

Multiply 2 and 5 to get 10.

$$12+12x+10x+12\left(\frac{x}{4}-8\right)\times 2=6048$$

Combine 12x and 10x to get 22x.

$$12+22x+12\left(\frac{x}{4}-8\right)\times 2=6048$$

Multiply 12 and 2 to get 24.

$$12+22x+24\left(\frac{x}{4}-8\right)=6048$$

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

$$12+22x+24\times \frac{x}{4}-192=6048$$

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

$$12+22x+6x-192=6048$$

Combine 22x and 6x to get 28x.

$$12+28x-192=6048$$

Subtract 192 from 12 to get -180.

$$-180+28x=6048$$

Add 180 to both sides.

$$28x=6048+180$$

Add 6048 and 180 to get 6228.

$$28x=6228$$

Divide both sides by 28.

$$x=\frac{6228}{28}$$

Reduce the fraction \frac{6228}{28} to lowest terms by extracting and canceling out 4.

$$x=\frac{1557}{7}$$