Solve 2/3(x+3)-2/3(2x+5)+1/3(41x-5)=1/12

$$\frac { 2 } { 3 } ( x + 3 ) - \frac { 2 } { 3 } ( 2 x + 5 ) + \frac { 1 } { 3 } ( 41 x - 5 ) = \frac { 1 } { 12 }$$

Solve for x

$$x=\frac{37}{156}\approx 0.237179487$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{2}{3} by x+3.

$$\frac{2}{3}x+\frac{2}{3}\times 3-\frac{2}{3}\left(2x+5\right)+\frac{1}{3}\left(41x-5\right)=\frac{1}{12}$$

Cancel out 3 and 3.

$$\frac{2}{3}x+2-\frac{2}{3}\left(2x+5\right)+\frac{1}{3}\left(41x-5\right)=\frac{1}{12}$$

Use the distributive property to multiply -\frac{2}{3} by 2x+5.

$$\frac{2}{3}x+2-\frac{2}{3}\times 2x-\frac{2}{3}\times 5+\frac{1}{3}\left(41x-5\right)=\frac{1}{12}$$

Express -\frac{2}{3}\times 2 as a single fraction.

$$\frac{2}{3}x+2+\frac{-2\times 2}{3}x-\frac{2}{3}\times 5+\frac{1}{3}\left(41x-5\right)=\frac{1}{12}$$

Multiply -2 and 2 to get -4.

$$\frac{2}{3}x+2+\frac{-4}{3}x-\frac{2}{3}\times 5+\frac{1}{3}\left(41x-5\right)=\frac{1}{12}$$

Fraction \frac{-4}{3} can be rewritten as -\frac{4}{3} by extracting the negative sign.

$$\frac{2}{3}x+2-\frac{4}{3}x-\frac{2}{3}\times 5+\frac{1}{3}\left(41x-5\right)=\frac{1}{12}$$

Express -\frac{2}{3}\times 5 as a single fraction.

$$\frac{2}{3}x+2-\frac{4}{3}x+\frac{-2\times 5}{3}+\frac{1}{3}\left(41x-5\right)=\frac{1}{12}$$

Multiply -2 and 5 to get -10.

$$\frac{2}{3}x+2-\frac{4}{3}x+\frac{-10}{3}+\frac{1}{3}\left(41x-5\right)=\frac{1}{12}$$

Fraction \frac{-10}{3} can be rewritten as -\frac{10}{3} by extracting the negative sign.

$$\frac{2}{3}x+2-\frac{4}{3}x-\frac{10}{3}+\frac{1}{3}\left(41x-5\right)=\frac{1}{12}$$

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

$$-\frac{2}{3}x+2-\frac{10}{3}+\frac{1}{3}\left(41x-5\right)=\frac{1}{12}$$

Convert 2 to fraction \frac{6}{3}.

$$-\frac{2}{3}x+\frac{6}{3}-\frac{10}{3}+\frac{1}{3}\left(41x-5\right)=\frac{1}{12}$$

Since \frac{6}{3} and \frac{10}{3} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{2}{3}x+\frac{6-10}{3}+\frac{1}{3}\left(41x-5\right)=\frac{1}{12}$$

Subtract 10 from 6 to get -4.

$$-\frac{2}{3}x-\frac{4}{3}+\frac{1}{3}\left(41x-5\right)=\frac{1}{12}$$

Use the distributive property to multiply \frac{1}{3} by 41x-5.

$$-\frac{2}{3}x-\frac{4}{3}+\frac{1}{3}\times 41x+\frac{1}{3}\left(-5\right)=\frac{1}{12}$$

Multiply \frac{1}{3} and 41 to get \frac{41}{3}.

$$-\frac{2}{3}x-\frac{4}{3}+\frac{41}{3}x+\frac{1}{3}\left(-5\right)=\frac{1}{12}$$

Multiply \frac{1}{3} and -5 to get \frac{-5}{3}.

$$-\frac{2}{3}x-\frac{4}{3}+\frac{41}{3}x+\frac{-5}{3}=\frac{1}{12}$$

Fraction \frac{-5}{3} can be rewritten as -\frac{5}{3} by extracting the negative sign.

$$-\frac{2}{3}x-\frac{4}{3}+\frac{41}{3}x-\frac{5}{3}=\frac{1}{12}$$

Combine -\frac{2}{3}x and \frac{41}{3}x to get 13x.

$$13x-\frac{4}{3}-\frac{5}{3}=\frac{1}{12}$$

Since -\frac{4}{3} and \frac{5}{3} have the same denominator, subtract them by subtracting their numerators.

$$13x+\frac{-4-5}{3}=\frac{1}{12}$$

Subtract 5 from -4 to get -9.

$$13x+\frac{-9}{3}=\frac{1}{12}$$

Divide -9 by 3 to get -3.

$$13x-3=\frac{1}{12}$$

Add 3 to both sides.

$$13x=\frac{1}{12}+3$$

Convert 3 to fraction \frac{36}{12}.

$$13x=\frac{1}{12}+\frac{36}{12}$$

Since \frac{1}{12} and \frac{36}{12} have the same denominator, add them by adding their numerators.

$$13x=\frac{1+36}{12}$$

Add 1 and 36 to get 37.

$$13x=\frac{37}{12}$$

Divide both sides by 13.

$$x=\frac{\frac{37}{12}}{13}$$

Express \frac{\frac{37}{12}}{13} as a single fraction.

$$x=\frac{37}{12\times 13}$$

Multiply 12 and 13 to get 156.

$$x=\frac{37}{156}$$