Solve for b 6=|-b+5|

$6 = | - b + 5 |$

Rewrite the equation as $| - b + 5 | = 6$ .

$| - b + 5 | = 6$

Remove the absolute value term. This creates a $\pm$ on the right side of the equation because $| x | = \pm x$ .

$- b + 5 = \pm 6$

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$- b + 5 = 6$

Move all terms not containing $b$ to the right side of the equation.

Subtract $5$ from both sides of the equation.

$- b = 6 - 5$

Subtract $5$ from $6$ .

$- b = 1$

Divide each term in $- b = 1$ by $- 1$ and simplify.

Divide each term in $- b = 1$ by $- 1$ .

$\frac{- b}{- 1} = \frac{1}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{b}{1} = \frac{1}{- 1}$

Divide $b$ by $1$ .

$b = \frac{1}{- 1}$

Simplify the right side.

Divide $1$ by $- 1$ .

$b = - 1$

Next, use the negative value of the $\pm$ to find the second solution.

$- b + 5 = - 6$

Move all terms not containing $b$ to the right side of the equation.

Subtract $5$ from both sides of the equation.

$- b = - 6 - 5$

Subtract $5$ from $- 6$ .

$- b = - 11$

Divide each term in $- b = - 11$ by $- 1$ and simplify.

Divide each term in $- b = - 11$ by $- 1$ .

$\frac{- b}{- 1} = \frac{- 11}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{b}{1} = \frac{- 11}{- 1}$

Divide $b$ by $1$ .

$b = \frac{- 11}{- 1}$

Simplify the right side.

Divide $- 11$ by $- 1$ .

$b = 11$

The complete solution is the result of both the positive and negative portions of the solution.

$b = - 1, 11$