Solve 1/3(x+1)-3/4(x-2)=1/6

$$\frac { 1 } { 3 } ( x + 1 ) - \frac { 3 } { 4 } ( x - 2 ) = \frac { 1 } { 6 }$$

Solve for x

$$x=4$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{1}{3} by x+1.

$$\frac{1}{3}x+\frac{1}{3}-\frac{3}{4}\left(x-2\right)=\frac{1}{6}$$

Use the distributive property to multiply -\frac{3}{4} by x-2.

$$\frac{1}{3}x+\frac{1}{3}-\frac{3}{4}x-\frac{3}{4}\left(-2\right)=\frac{1}{6}$$

Express -\frac{3}{4}\left(-2\right) as a single fraction.

$$\frac{1}{3}x+\frac{1}{3}-\frac{3}{4}x+\frac{-3\left(-2\right)}{4}=\frac{1}{6}$$

Multiply -3 and -2 to get 6.

$$\frac{1}{3}x+\frac{1}{3}-\frac{3}{4}x+\frac{6}{4}=\frac{1}{6}$$

Reduce the fraction \frac{6}{4} to lowest terms by extracting and canceling out 2.

$$\frac{1}{3}x+\frac{1}{3}-\frac{3}{4}x+\frac{3}{2}=\frac{1}{6}$$

Combine \frac{1}{3}x and -\frac{3}{4}x to get -\frac{5}{12}x.

$$-\frac{5}{12}x+\frac{1}{3}+\frac{3}{2}=\frac{1}{6}$$

Least common multiple of 3 and 2 is 6. Convert \frac{1}{3} and \frac{3}{2} to fractions with denominator 6.

$$-\frac{5}{12}x+\frac{2}{6}+\frac{9}{6}=\frac{1}{6}$$

Since \frac{2}{6} and \frac{9}{6} have the same denominator, add them by adding their numerators.

$$-\frac{5}{12}x+\frac{2+9}{6}=\frac{1}{6}$$

Add 2 and 9 to get 11.

$$-\frac{5}{12}x+\frac{11}{6}=\frac{1}{6}$$

Subtract \frac{11}{6} from both sides.

$$-\frac{5}{12}x=\frac{1}{6}-\frac{11}{6}$$

Since \frac{1}{6} and \frac{11}{6} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{5}{12}x=\frac{1-11}{6}$$

Subtract 11 from 1 to get -10.

$$-\frac{5}{12}x=\frac{-10}{6}$$

Reduce the fraction \frac{-10}{6} to lowest terms by extracting and canceling out 2.

$$-\frac{5}{12}x=-\frac{5}{3}$$

Multiply both sides by -\frac{12}{5}, the reciprocal of -\frac{5}{12}.

$$x=-\frac{5}{3}\left(-\frac{12}{5}\right)$$

Multiply -\frac{5}{3} times -\frac{12}{5} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{-5\left(-12\right)}{3\times 5}.

$$x=\frac{60}{15}$$

Divide 60 by 15 to get 4.

$$x=4$$