Solve for b 33=|b-4|

$33 = | b - 4 |$

Rewrite the equation as $| b - 4 | = 33$ .

$| b - 4 | = 33$

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

$b - 4 = \pm 33$

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.

$b - 4 = 33$

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

Add $4$ to both sides of the equation.

$b = 33 + 4$

Add $33$ and $4$ .

$b = 37$

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

$b - 4 = - 33$

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

Add $4$ to both sides of the equation.

$b = - 33 + 4$

Add $- 33$ and $4$ .

$b = - 29$

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

$b = 37, - 29$