Solve 5(x-2)/12+2/4-(27+x)/36=x+20-(4-x)/12-frac{(20+3x)}{18}

$$\frac { 5 ( x - 2 ) } { 12 } + \frac { 2 } { 4 } - \frac { ( 27 + x ) } { 36 } = x + 20 - \frac { ( 4 - x ) } { 12 } - \frac { ( 20 + 3 x ) } { 18 }$$

Solve for x

$$x = -\frac{707}{19} = -37\frac{4}{19} \approx -37.210526316$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 36, the least common multiple of 12,4,36,18.

$$3\times 5\left(x-2\right)+9\times 2-\left(27+x\right)=36x+720-3\left(4-x\right)-2\left(20+3x\right)$$

Multiply 3 and 5 to get 15.

$$15\left(x-2\right)+9\times 2-\left(27+x\right)=36x+720-3\left(4-x\right)-2\left(20+3x\right)$$

Use the distributive property to multiply 15 by x-2.

$$15x-30+9\times 2-\left(27+x\right)=36x+720-3\left(4-x\right)-2\left(20+3x\right)$$

Multiply 9 and 2 to get 18.

$$15x-30+18-\left(27+x\right)=36x+720-3\left(4-x\right)-2\left(20+3x\right)$$

Add -30 and 18 to get -12.

$$15x-12-\left(27+x\right)=36x+720-3\left(4-x\right)-2\left(20+3x\right)$$

To find the opposite of 27+x, find the opposite of each term.

$$15x-12-27-x=36x+720-3\left(4-x\right)-2\left(20+3x\right)$$

Subtract 27 from -12 to get -39.

$$15x-39-x=36x+720-3\left(4-x\right)-2\left(20+3x\right)$$

Combine 15x and -x to get 14x.

$$14x-39=36x+720-3\left(4-x\right)-2\left(20+3x\right)$$

Use the distributive property to multiply -3 by 4-x.

$$14x-39=36x+720-12+3x-2\left(20+3x\right)$$

Subtract 12 from 720 to get 708.

$$14x-39=36x+708+3x-2\left(20+3x\right)$$

Combine 36x and 3x to get 39x.

$$14x-39=39x+708-2\left(20+3x\right)$$

Use the distributive property to multiply -2 by 20+3x.

$$14x-39=39x+708-40-6x$$

Subtract 40 from 708 to get 668.

$$14x-39=39x+668-6x$$

Combine 39x and -6x to get 33x.

$$14x-39=33x+668$$

Subtract 33x from both sides.

$$14x-39-33x=668$$

Combine 14x and -33x to get -19x.

$$-19x-39=668$$

Add 39 to both sides.

$$-19x=668+39$$

Add 668 and 39 to get 707.

$$-19x=707$$

Divide both sides by -19.

$$x=\frac{707}{-19}$$

Fraction \frac{707}{-19} can be rewritten as -\frac{707}{19} by extracting the negative sign.

$$x=-\frac{707}{19}$$