Finite Math Examples

$y = | x - 2 | + 3$

Step 1

Rewrite the equation as $| x - 2 | + 3 = y$ .

$| x - 2 | + 3 = y$

Step 2

Subtract $3$ from both sides of the equation.

$| x - 2 | = y - 3$

Step 3

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

$x - 2 = \pm (y - 3)$

Step 4

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

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Step 4.1

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

$x - 2 = y - 3$

Step 4.2

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

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Step 4.2.1

Add $2$ to both sides of the equation.

$x = y - 3 + 2$

Step 4.2.2

Add $- 3$ and $2$ .

$x = y - 1$

Step 4.3

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

$x - 2 = - (y - 3)$

Step 4.4

Simplify $- (y - 3)$ .

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Step 4.4.1

Rewrite.

$x - 2 = 0 + 0 - (y - 3)$

Step 4.4.2

Simplify by adding zeros.

$x - 2 = - (y - 3)$

Step 4.4.3

Apply the distributive property.

$x - 2 = - y - - 3$

Step 4.4.4

Multiply $- 1$ by $- 3$ .

$x - 2 = - y + 3$

Step 4.5

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

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Step 4.5.1

Add $2$ to both sides of the equation.

$x = - y + 3 + 2$

Step 4.5.2

Add $3$ and $2$ .

$x = - y + 5$

Step 4.6

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

$x = y - 1$

$x = - y + 5$

$x = y - 1$

$x = - y + 5$