Solve x+7/6(x+1/6)=5/3x+37/36

$$x + \frac { 7 } { 6 } ( x + \frac { 1 } { 6 } ) = \frac { 5 } { 3 } x + \frac { 37 } { 36 }$$

Solve for x

$$x = \frac{5}{3} = 1\frac{2}{3} \approx 1.666666667$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{7}{6} by x+\frac{1}{6}.

$$x+\frac{7}{6}x+\frac{7}{6}\times \frac{1}{6}=\frac{5}{3}x+\frac{37}{36}$$

Multiply \frac{7}{6} times \frac{1}{6} by multiplying numerator times numerator and denominator times denominator.

$$x+\frac{7}{6}x+\frac{7\times 1}{6\times 6}=\frac{5}{3}x+\frac{37}{36}$$

Do the multiplications in the fraction \frac{7\times 1}{6\times 6}.

$$x+\frac{7}{6}x+\frac{7}{36}=\frac{5}{3}x+\frac{37}{36}$$

Combine x and \frac{7}{6}x to get \frac{13}{6}x.

$$\frac{13}{6}x+\frac{7}{36}=\frac{5}{3}x+\frac{37}{36}$$

Subtract \frac{5}{3}x from both sides.

$$\frac{13}{6}x+\frac{7}{36}-\frac{5}{3}x=\frac{37}{36}$$

Combine \frac{13}{6}x and -\frac{5}{3}x to get \frac{1}{2}x.

$$\frac{1}{2}x+\frac{7}{36}=\frac{37}{36}$$

Subtract \frac{7}{36} from both sides.

$$\frac{1}{2}x=\frac{37}{36}-\frac{7}{36}$$

Since \frac{37}{36} and \frac{7}{36} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{2}x=\frac{37-7}{36}$$

Subtract 7 from 37 to get 30.

$$\frac{1}{2}x=\frac{30}{36}$$

Reduce the fraction \frac{30}{36} to lowest terms by extracting and canceling out 6.

$$\frac{1}{2}x=\frac{5}{6}$$

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

$$x=\frac{5}{6}\times 2$$

Express \frac{5}{6}\times 2 as a single fraction.

$$x=\frac{5\times 2}{6}$$

Multiply 5 and 2 to get 10.

$$x=\frac{10}{6}$$

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

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