Trigonometry Examples

$| 6 x - 7 | = 5$

Step 1

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

$6 x - 7 = \pm 5$

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.

$6 x - 7 = 5$

Step 2.2

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

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Step 2.2.1

Add $7$ to both sides of the equation.

$6 x = 5 + 7$

Step 2.2.2

Add $5$ and $7$ .

$6 x = 12$

Step 2.3

Divide each term in $6 x = 12$ by $6$ and simplify.

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Step 2.3.1

Divide each term in $6 x = 12$ by $6$ .

$\frac{6 x}{6} = \frac{12}{6}$

Step 2.3.2

Simplify the left side.

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Step 2.3.2.1

Cancel the common factor of $6$ .

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Step 2.3.2.1.1

Cancel the common factor.

$\frac{6 x}{6} = \frac{12}{6}$

Step 2.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{12}{6}$

Step 2.3.3

Simplify the right side.

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Step 2.3.3.1

Divide $12$ by $6$ .

$x = 2$

Step 2.4

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

$6 x - 7 = - 5$

Step 2.5

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

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Step 2.5.1

Add $7$ to both sides of the equation.

$6 x = - 5 + 7$

Step 2.5.2

Add $- 5$ and $7$ .

$6 x = 2$

Step 2.6

Divide each term in $6 x = 2$ by $6$ and simplify.

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Step 2.6.1

Divide each term in $6 x = 2$ by $6$ .

$\frac{6 x}{6} = \frac{2}{6}$

Step 2.6.2

Simplify the left side.

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Step 2.6.2.1

Cancel the common factor of $6$ .

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Step 2.6.2.1.1

Cancel the common factor.

$\frac{6 x}{6} = \frac{2}{6}$

Step 2.6.2.1.2

Divide $x$ by $1$ .

$x = \frac{2}{6}$

Step 2.6.3

Simplify the right side.

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Step 2.6.3.1

Cancel the common factor of $2$ and $6$ .

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Step 2.6.3.1.1

Factor $2$ out of $2$ .

$x = \frac{2 (1)}{6}$

Step 2.6.3.1.2

Cancel the common factors.

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Step 2.6.3.1.2.1

Factor $2$ out of $6$ .

$x = \frac{2 \cdot 1}{2 \cdot 3}$

Step 2.6.3.1.2.2

Cancel the common factor.

$x = \frac{2 \cdot 1}{2 \cdot 3}$

Step 2.6.3.1.2.3

Rewrite the expression.

$x = \frac{1}{3}$

Step 2.7

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

$x = 2, \frac{1}{3}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = 2, \frac{1}{3}$

Decimal Form:

$x = 2, 0.\overline{3}$