Solve 11/5left(x+1/2right)=5/3+1/6

$$\frac{ 11 }{ 5 } \left( x+ \frac{ 1 }{ 2 } \right) = \frac{ 5 }{ 3 } + \frac{ 1 }{ 6 }$$

Solve for x

$$x=\frac{1}{3}\approx 0.333333333$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{11}{5} by x+\frac{1}{2}.

$$\frac{11}{5}x+\frac{11}{5}\times \frac{1}{2}=\frac{5}{3}+\frac{1}{6}$$

Multiply \frac{11}{5} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{11}{5}x+\frac{11\times 1}{5\times 2}=\frac{5}{3}+\frac{1}{6}$$

Do the multiplications in the fraction \frac{11\times 1}{5\times 2}.

$$\frac{11}{5}x+\frac{11}{10}=\frac{5}{3}+\frac{1}{6}$$

Least common multiple of 3 and 6 is 6. Convert \frac{5}{3} and \frac{1}{6} to fractions with denominator 6.

$$\frac{11}{5}x+\frac{11}{10}=\frac{10}{6}+\frac{1}{6}$$

Since \frac{10}{6} and \frac{1}{6} have the same denominator, add them by adding their numerators.

$$\frac{11}{5}x+\frac{11}{10}=\frac{10+1}{6}$$

Add 10 and 1 to get 11.

$$\frac{11}{5}x+\frac{11}{10}=\frac{11}{6}$$

Subtract \frac{11}{10} from both sides.

$$\frac{11}{5}x=\frac{11}{6}-\frac{11}{10}$$

Least common multiple of 6 and 10 is 30. Convert \frac{11}{6} and \frac{11}{10} to fractions with denominator 30.

$$\frac{11}{5}x=\frac{55}{30}-\frac{33}{30}$$

Since \frac{55}{30} and \frac{33}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{11}{5}x=\frac{55-33}{30}$$

Subtract 33 from 55 to get 22.

$$\frac{11}{5}x=\frac{22}{30}$$

Reduce the fraction \frac{22}{30} to lowest terms by extracting and canceling out 2.

$$\frac{11}{5}x=\frac{11}{15}$$

Multiply both sides by \frac{5}{11}, the reciprocal of \frac{11}{5}.

$$x=\frac{11}{15}\times \frac{5}{11}$$

Multiply \frac{11}{15} times \frac{5}{11} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{11\times 5}{15\times 11}$$

Cancel out 11 in both numerator and denominator.

$$x=\frac{5}{15}$$

Reduce the fraction \frac{5}{15} to lowest terms by extracting and canceling out 5.

$$x=\frac{1}{3}$$