Trigonometry Examples

$| 7 x - 3 | = 8$

Step 1

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

$7 x - 3 = \pm 8$

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.

$7 x - 3 = 8$

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 $3$ to both sides of the equation.

$7 x = 8 + 3$

Step 2.2.2

Add $8$ and $3$ .

$7 x = 11$

Step 2.3

Divide each term in $7 x = 11$ by $7$ and simplify.

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Step 2.3.1

Divide each term in $7 x = 11$ by $7$ .

$\frac{7 x}{7} = \frac{11}{7}$

Step 2.3.2

Simplify the left side.

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Step 2.3.2.1

Cancel the common factor of $7$ .

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Step 2.3.2.1.1

Cancel the common factor.

$\frac{7 x}{7} = \frac{11}{7}$

Step 2.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{11}{7}$

Step 2.4

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

$7 x - 3 = - 8$

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 $3$ to both sides of the equation.

$7 x = - 8 + 3$

Step 2.5.2

Add $- 8$ and $3$ .

$7 x = - 5$

Step 2.6

Divide each term in $7 x = - 5$ by $7$ and simplify.

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Step 2.6.1

Divide each term in $7 x = - 5$ by $7$ .

$\frac{7 x}{7} = \frac{- 5}{7}$

Step 2.6.2

Simplify the left side.

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Step 2.6.2.1

Cancel the common factor of $7$ .

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Step 2.6.2.1.1

Cancel the common factor.

$\frac{7 x}{7} = \frac{- 5}{7}$

Step 2.6.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 5}{7}$

Step 2.6.3

Simplify the right side.

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Step 2.6.3.1

Move the negative in front of the fraction.

$x = - \frac{5}{7}$

Step 2.7

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

$x = \frac{11}{7}, - \frac{5}{7}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = \frac{11}{7}, - \frac{5}{7}$

Decimal Form:

$x = 1.\overline{571428}, - 0.\overline{714285}$

Mixed Number Form:

$x = 1 \frac{4}{7}, - \frac{5}{7}$