Solve x+1/2-5x+9/28=x+6/21+5-x-12/3

$$\frac { x + 1 } { 2 } - \frac { 5 x + 9 } { 28 } = \frac { x + 6 } { 21 } + 5 - \frac { x - 12 } { 3 }$$

Solve for x

$$x=15$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 84, the least common multiple of 2,28,21,3.

$$42\left(x+1\right)-3\left(5x+9\right)=4\left(x+6\right)+420-28\left(x-12\right)$$

Use the distributive property to multiply 42 by x+1.

$$42x+42-3\left(5x+9\right)=4\left(x+6\right)+420-28\left(x-12\right)$$

Use the distributive property to multiply -3 by 5x+9.

$$42x+42-15x-27=4\left(x+6\right)+420-28\left(x-12\right)$$

Combine 42x and -15x to get 27x.

$$27x+42-27=4\left(x+6\right)+420-28\left(x-12\right)$$

Subtract 27 from 42 to get 15.

$$27x+15=4\left(x+6\right)+420-28\left(x-12\right)$$

Use the distributive property to multiply 4 by x+6.

$$27x+15=4x+24+420-28\left(x-12\right)$$

Add 24 and 420 to get 444.

$$27x+15=4x+444-28\left(x-12\right)$$

Use the distributive property to multiply -28 by x-12.

$$27x+15=4x+444-28x+336$$

Combine 4x and -28x to get -24x.

$$27x+15=-24x+444+336$$

Add 444 and 336 to get 780.

$$27x+15=-24x+780$$

Add 24x to both sides.

$$27x+15+24x=780$$

Combine 27x and 24x to get 51x.

$$51x+15=780$$

Subtract 15 from both sides.

$$51x=780-15$$

Subtract 15 from 780 to get 765.

$$51x=765$$

Divide both sides by 51.

$$x=\frac{765}{51}$$

Divide 765 by 51 to get 15.

$$x=15$$