Solve x-3=1/6(x-3+b+8)

$$x - 3 = \frac { 1 } { 6 } ( x - 3 + b + 8 )$$

Solve for b

$$b=5x-23$$

Steps for Solving Linear Equation

Add -3 and 8 to get 5.

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

Use the distributive property to multiply \frac{1}{6} by x+5+b.

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

Swap sides so that all variable terms are on the left hand side.

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

Subtract \frac{1}{6}x from both sides.

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

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

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

Subtract \frac{5}{6} from both sides.

$$\frac{1}{6}b=\frac{5}{6}x-3-\frac{5}{6}$$

Subtract \frac{5}{6} from -3 to get -\frac{23}{6}.

$$\frac{1}{6}b=\frac{5}{6}x-\frac{23}{6}$$

The equation is in standard form.

$$\frac{1}{6}b=\frac{5x-23}{6}$$

Multiply both sides by 6.

$$\frac{\frac{1}{6}b}{\frac{1}{6}}=\frac{5x-23}{\frac{1}{6}\times 6}$$

Dividing by \frac{1}{6} undoes the multiplication by \frac{1}{6}.

$$b=\frac{5x-23}{\frac{1}{6}\times 6}$$

Divide \frac{5x-23}{6} by \frac{1}{6} by multiplying \frac{5x-23}{6} by the reciprocal of \frac{1}{6}.

$$b=5x-23$$

Solve for x

$$x=\frac{b+23}{5}$$

Steps for Solving Linear Equation

Add -3 and 8 to get 5.

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

Use the distributive property to multiply \frac{1}{6} by x+5+b.

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

Subtract \frac{1}{6}x from both sides.

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

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

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

Add 3 to both sides.

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

Add \frac{5}{6} and 3 to get \frac{23}{6}.

$$\frac{5}{6}x=\frac{23}{6}+\frac{1}{6}b$$

The equation is in standard form.

$$\frac{5}{6}x=\frac{b+23}{6}$$

Divide both sides of the equation by \frac{5}{6}, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{\frac{5}{6}x}{\frac{5}{6}}=\frac{b+23}{\frac{5}{6}\times 6}$$

Dividing by \frac{5}{6} undoes the multiplication by \frac{5}{6}.

$$x=\frac{b+23}{\frac{5}{6}\times 6}$$

Divide \frac{23+b}{6} by \frac{5}{6} by multiplying \frac{23+b}{6} by the reciprocal of \frac{5}{6}.

$$x=\frac{b+23}{5}$$