Trigonometry Examples

$| x - 1 | + | y | = 2$

Step 1

Subtract $| y |$ from both sides of the equation.

$| x - 1 | = 2 - | y |$

Step 2

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

$x - 1 = \pm (2 - | y |)$

Step 3

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

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Step 3.1

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

$x - 1 = 2 - | y |$

Step 3.2

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

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Step 3.2.1

Add $1$ to both sides of the equation.

$x = 2 - | y | + 1$

Step 3.2.2

Add $2$ and $1$ .

$x = 3 - | y |$

Step 3.3

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

$x - 1 = - (2 - | y |)$

Step 3.4

Simplify $- (2 - | y |)$ .

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Step 3.4.1

Rewrite.

$x - 1 = 0 + 0 - (2 - | y |)$

Step 3.4.2

Simplify by adding zeros.

$x - 1 = - (2 - | y |)$

Step 3.4.3

Apply the distributive property.

$x - 1 = - 1 \cdot 2 - - | y |$

Step 3.4.4

Multiply $- 1$ by $2$ .

$x - 1 = - 2 - - | y |$

Step 3.4.5

Multiply $- - | y |$ .

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Step 3.4.5.1

Multiply $- 1$ by $- 1$ .

$x - 1 = - 2 + 1 | y |$

Step 3.4.5.2

Multiply $| y |$ by $1$ .

$x - 1 = - 2 + | y |$

Step 3.5

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

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Step 3.5.1

Add $1$ to both sides of the equation.

$x = - 2 + | y | + 1$

Step 3.5.2

Add $- 2$ and $1$ .

$x = - 1 + | y |$

Step 3.6

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

$x = 3 - | y |$

$x = - 1 + | y |$

$x = 3 - | y |$

$x = - 1 + | y |$

Step 4