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

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

Solve for x

$$x = \frac{31}{9} = 3\frac{4}{9} \approx 3.444444444$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{1}{2} by x+1.

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

Multiply \frac{4}{3} times \frac{1}{6} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{4\times 1}{3\times 6}.

$$\frac{1}{2}x+\frac{1}{2}-\frac{4}{18}=2$$

Reduce the fraction \frac{4}{18} to lowest terms by extracting and canceling out 2.

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

Least common multiple of 2 and 9 is 18. Convert \frac{1}{2} and \frac{2}{9} to fractions with denominator 18.

$$\frac{1}{2}x+\frac{9}{18}-\frac{4}{18}=2$$

Since \frac{9}{18} and \frac{4}{18} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{2}x+\frac{9-4}{18}=2$$

Subtract 4 from 9 to get 5.

$$\frac{1}{2}x+\frac{5}{18}=2$$

Subtract \frac{5}{18} from both sides.

$$\frac{1}{2}x=2-\frac{5}{18}$$

Convert 2 to fraction \frac{36}{18}.

$$\frac{1}{2}x=\frac{36}{18}-\frac{5}{18}$$

Since \frac{36}{18} and \frac{5}{18} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{2}x=\frac{36-5}{18}$$

Subtract 5 from 36 to get 31.

$$\frac{1}{2}x=\frac{31}{18}$$

Multiply both sides by 2, the reciprocal of \frac{1}{2}.

$$x=\frac{31}{18}\times 2$$

Express \frac{31}{18}\times 2 as a single fraction.

$$x=\frac{31\times 2}{18}$$

Multiply 31 and 2 to get 62.

$$x=\frac{62}{18}$$

Reduce the fraction \frac{62}{18} to lowest terms by extracting and canceling out 2.

$$x=\frac{31}{9}$$