Solve for b |14-b|=17

$| 14 - b | = 17$

Step 1

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

$14 - b = \pm 17$

Step 2

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.

$14 - b = 17$

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

Subtract $14$ from both sides of the equation.

$- b = 17 - 14$

Subtract $14$ from $17$ .

$- b = 3$

Divide each term in $- b = 3$ by $- 1$ and simplify.

Divide each term in $- b = 3$ by $- 1$ .

$\frac{- b}{- 1} = \frac{3}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{b}{1} = \frac{3}{- 1}$

Divide $b$ by $1$ .

$b = \frac{3}{- 1}$

Simplify the right side.

Divide $3$ by $- 1$ .

$b = - 3$

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

$14 - b = - 17$

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

Subtract $14$ from both sides of the equation.

$- b = - 17 - 14$

Subtract $14$ from $- 17$ .

$- b = - 31$

Divide each term in $- b = - 31$ by $- 1$ and simplify.

Divide each term in $- b = - 31$ by $- 1$ .

$\frac{- b}{- 1} = \frac{- 31}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{b}{1} = \frac{- 31}{- 1}$

Divide $b$ by $1$ .

$b = \frac{- 31}{- 1}$

Simplify the right side.

Divide $- 31$ by $- 1$ .

$b = 31$

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

$b = - 3, 31$