Solve 5+2/3x/24+1/3x/72=frac{frac{1}{4}x}{24}+frac{frac{3}{4}x}{72}

$$5 + \frac { \frac { 2 } { 3 } x } { 24 } + \frac { \frac { 1 } { 3 } x } { 72 } = \frac { \frac { 1 } { 4 } x } { 24 } + \frac { \frac { 3 } { 4 } x } { 72 }$$

Solve for x

$$x=-432$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 72, the least common multiple of 24,72.

$$360+3\times \frac{2}{3}x+\frac{1}{3}x=3\times \frac{1}{4}x+\frac{3}{4}x$$

Cancel out 3 and 3.

$$360+2x+\frac{1}{3}x=3\times \frac{1}{4}x+\frac{3}{4}x$$

Combine 2x and \frac{1}{3}x to get \frac{7}{3}x.

$$360+\frac{7}{3}x=3\times \frac{1}{4}x+\frac{3}{4}x$$

Multiply 3 and \frac{1}{4} to get \frac{3}{4}.

$$360+\frac{7}{3}x=\frac{3}{4}x+\frac{3}{4}x$$

Combine \frac{3}{4}x and \frac{3}{4}x to get \frac{3}{2}x.

$$360+\frac{7}{3}x=\frac{3}{2}x$$

Subtract \frac{3}{2}x from both sides.

$$360+\frac{7}{3}x-\frac{3}{2}x=0$$

Combine \frac{7}{3}x and -\frac{3}{2}x to get \frac{5}{6}x.

$$360+\frac{5}{6}x=0$$

Subtract 360 from both sides. Anything subtracted from zero gives its negation.

$$\frac{5}{6}x=-360$$

Multiply both sides by \frac{6}{5}, the reciprocal of \frac{5}{6}.

$$x=-360\times \frac{6}{5}$$

Express -360\times \frac{6}{5} as a single fraction.

$$x=\frac{-360\times 6}{5}$$

Multiply -360 and 6 to get -2160.

$$x=\frac{-2160}{5}$$

Divide -2160 by 5 to get -432.

$$x=-432$$