Solve 1/4left(12x/5-8/3right)+11x/6=frac{5}{6}left(frac{4x}{15}-frac{9}{10}right)+frac{11}{6}+frac{3x}{4}

$$\frac{ 1 }{ 4 } \left( \frac{ 12x }{ 5 } - \frac{ 8 }{ 3 } \right) + \frac{ 11x }{ 6 } = \frac{ 5 }{ 6 } \left( \frac{ 4x }{ 15 } - \frac{ 9 }{ 10 } \right) + \frac{ 11 }{ 6 } + \frac{ 3x }{ 4 }$$

Solve for x

$$x = \frac{315}{263} = 1\frac{52}{263} \approx 1.197718631$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 60, the least common multiple of 4,5,3,6,15,10.

$$15\left(\frac{12x}{5}-\frac{8}{3}\right)+10\times 11x=50\left(\frac{4x}{15}-\frac{9}{10}\right)+110+15\times 3x$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 5 and 3 is 15. Multiply \frac{12x}{5} times \frac{3}{3}. Multiply \frac{8}{3} times \frac{5}{5}.

$$15\left(\frac{3\times 12x}{15}-\frac{8\times 5}{15}\right)+10\times 11x=50\left(\frac{4x}{15}-\frac{9}{10}\right)+110+15\times 3x$$

Since \frac{3\times 12x}{15} and \frac{8\times 5}{15} have the same denominator, subtract them by subtracting their numerators.

$$15\times \frac{3\times 12x-8\times 5}{15}+10\times 11x=50\left(\frac{4x}{15}-\frac{9}{10}\right)+110+15\times 3x$$

Do the multiplications in 3\times 12x-8\times 5.

$$15\times \frac{36x-40}{15}+10\times 11x=50\left(\frac{4x}{15}-\frac{9}{10}\right)+110+15\times 3x$$

Express 15\times \frac{36x-40}{15} as a single fraction.

$$\frac{15\left(36x-40\right)}{15}+10\times 11x=50\left(\frac{4x}{15}-\frac{9}{10}\right)+110+15\times 3x$$

Cancel out 15 and 15.

$$36x-40+10\times 11x=50\left(\frac{4x}{15}-\frac{9}{10}\right)+110+15\times 3x$$

Multiply 10 and 11 to get 110.

$$36x-40+110x=50\left(\frac{4x}{15}-\frac{9}{10}\right)+110+15\times 3x$$

Combine 36x and 110x to get 146x.

$$146x-40=50\left(\frac{4x}{15}-\frac{9}{10}\right)+110+15\times 3x$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 15 and 10 is 30. Multiply \frac{4x}{15} times \frac{2}{2}. Multiply \frac{9}{10} times \frac{3}{3}.

$$146x-40=50\left(\frac{2\times 4x}{30}-\frac{9\times 3}{30}\right)+110+15\times 3x$$

Since \frac{2\times 4x}{30} and \frac{9\times 3}{30} have the same denominator, subtract them by subtracting their numerators.

$$146x-40=50\times \frac{2\times 4x-9\times 3}{30}+110+15\times 3x$$

Do the multiplications in 2\times 4x-9\times 3.

$$146x-40=50\times \frac{8x-27}{30}+110+15\times 3x$$

Express 50\times \frac{8x-27}{30} as a single fraction.

$$146x-40=\frac{50\left(8x-27\right)}{30}+110+15\times 3x$$

Multiply 15 and 3 to get 45.

$$146x-40=\frac{50\left(8x-27\right)}{30}+110+45x$$

Use the distributive property to multiply 50 by 8x-27.

$$146x-40=\frac{400x-1350}{30}+110+45x$$

Divide each term of 400x-1350 by 30 to get \frac{40}{3}x-45.

$$146x-40=\frac{40}{3}x-45+110+45x$$

Add -45 and 110 to get 65.

$$146x-40=\frac{40}{3}x+65+45x$$

Combine \frac{40}{3}x and 45x to get \frac{175}{3}x.

$$146x-40=\frac{175}{3}x+65$$

Subtract \frac{175}{3}x from both sides.

$$146x-40-\frac{175}{3}x=65$$

Combine 146x and -\frac{175}{3}x to get \frac{263}{3}x.

$$\frac{263}{3}x-40=65$$

Add 40 to both sides.

$$\frac{263}{3}x=65+40$$

Add 65 and 40 to get 105.

$$\frac{263}{3}x=105$$

Multiply both sides by \frac{3}{263}, the reciprocal of \frac{263}{3}.

$$x=105\times \frac{3}{263}$$

Express 105\times \frac{3}{263} as a single fraction.

$$x=\frac{105\times 3}{263}$$

Multiply 105 and 3 to get 315.

$$x=\frac{315}{263}$$