Solve 4x/15+5x/6+6=7x/8-5x/12-frac{5}{9}+frac{139}{36}

$$\frac { 4 x } { 15 } + \frac { 5 x } { 6 } + 6 = \frac { 7 x } { 8 } - \frac { 5 x } { 12 } - \frac { 5 } { 9 } + \frac { 139 } { 36 }$$

Solve for x

$$x = -\frac{970}{231} = -4\frac{46}{231} \approx -4.199134199$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 360, the least common multiple of 15,6,8,12,9,36.

$$24\times 4x+60\times 5x+2160=45\times 7x-30\times 5x-200+1390$$

Multiply 24 and 4 to get 96.

$$96x+60\times 5x+2160=45\times 7x-30\times 5x-200+1390$$

Multiply 60 and 5 to get 300.

$$96x+300x+2160=45\times 7x-30\times 5x-200+1390$$

Combine 96x and 300x to get 396x.

$$396x+2160=45\times 7x-30\times 5x-200+1390$$

Multiply 45 and 7 to get 315. Multiply -30 and 5 to get -150.

$$396x+2160=315x-150x-200+1390$$

Combine 315x and -150x to get 165x.

$$396x+2160=165x-200+1390$$

Add -200 and 1390 to get 1190.

$$396x+2160=165x+1190$$

Subtract 165x from both sides.

$$396x+2160-165x=1190$$

Combine 396x and -165x to get 231x.

$$231x+2160=1190$$

Subtract 2160 from both sides.

$$231x=1190-2160$$

Subtract 2160 from 1190 to get -970.

$$231x=-970$$

Divide both sides by 231.

$$x=\frac{-970}{231}$$

Fraction \frac{-970}{231} can be rewritten as -\frac{970}{231} by extracting the negative sign.

$$x=-\frac{970}{231}$$