Precalculus Examples

$| a - 1 | = | b - 1 |$

Step 1

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

$a - 1 = \pm | b - 1 |$

Step 2

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

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Step 2.1

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

$a - 1 = | b - 1 |$

Step 2.2

Add $1$ to both sides of the equation.

$a = | b - 1 | + 1$

Step 2.3

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

$a - 1 = - | b - 1 |$

Step 2.4

Add $1$ to both sides of the equation.

$a = - | b - 1 | + 1$

Step 2.5

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

$a = | b - 1 | + 1$

$a = - | b - 1 | + 1$

$a = | b - 1 | + 1$

$a = - | b - 1 | + 1$