Trigonometry Examples

$| v + 7 | = 2$

Step 1

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

$v + 7 = \pm 2$

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.

$v + 7 = 2$

Step 2.2

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

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Step 2.2.1

Subtract $7$ from both sides of the equation.

$v = 2 - 7$

Step 2.2.2

Subtract $7$ from $2$ .

$v = - 5$

Step 2.3

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

$v + 7 = - 2$

Step 2.4

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

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Step 2.4.1

Subtract $7$ from both sides of the equation.

$v = - 2 - 7$

Step 2.4.2

Subtract $7$ from $- 2$ .

$v = - 9$

Step 2.5

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

$v = - 5, - 9$