Solve y(1/6)+1=(y+1)(1/7)

$$y ( \frac { 1 } { 6 } ) + 1 = ( y + 1 ) ( \frac { 1 } { 7 } )$$

Solve for y

$$y=-36$$

Steps for Solving Linear Equation

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

$$y\times \frac{1}{6}+1=y\times \frac{1}{7}+\frac{1}{7}$$

Subtract y\times \frac{1}{7} from both sides.

$$y\times \frac{1}{6}+1-y\times \frac{1}{7}=\frac{1}{7}$$

Combine y\times \frac{1}{6} and -y\times \frac{1}{7} to get \frac{1}{42}y.

$$\frac{1}{42}y+1=\frac{1}{7}$$

Subtract 1 from both sides.

$$\frac{1}{42}y=\frac{1}{7}-1$$

Convert 1 to fraction \frac{7}{7}.

$$\frac{1}{42}y=\frac{1}{7}-\frac{7}{7}$$

Since \frac{1}{7} and \frac{7}{7} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{42}y=\frac{1-7}{7}$$

Subtract 7 from 1 to get -6.

$$\frac{1}{42}y=-\frac{6}{7}$$

Multiply both sides by 42, the reciprocal of \frac{1}{42}.

$$y=-\frac{6}{7}\times 42$$

Express -\frac{6}{7}\times 42 as a single fraction.

$$y=\frac{-6\times 42}{7}$$

Multiply -6 and 42 to get -252.

$$y=\frac{-252}{7}$$

Divide -252 by 7 to get -36.

$$y=-36$$