Algebra Examples

$- 8 = - 3 | x - 5 | - 2$

Step 1

Rewrite the equation as $- 3 | x - 5 | - 2 = - 8$ .

$- 3 | x - 5 | - 2 = - 8$

Step 2

Move all terms not containing $| x - 5 |$ to the right side of the equation.

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Step 2.1

Add $2$ to both sides of the equation.

$- 3 | x - 5 | = - 8 + 2$

Step 2.2

Add $- 8$ and $2$ .

$- 3 | x - 5 | = - 6$

Step 3

Divide each term in $- 3 | x - 5 | = - 6$ by $- 3$ and simplify.

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Step 3.1

Divide each term in $- 3 | x - 5 | = - 6$ by $- 3$ .

$\frac{- 3 | x - 5 |}{- 3} = \frac{- 6}{- 3}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $- 3$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{- 3 | x - 5 |}{- 3} = \frac{- 6}{- 3}$

Step 3.2.1.2

Divide $| x - 5 |$ by $1$ .

$| x - 5 | = \frac{- 6}{- 3}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide $- 6$ by $- 3$ .

$| x - 5 | = 2$

Step 4

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

$x - 5 = \pm 2$

Step 5

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

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Step 5.1

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

$x - 5 = 2$

Step 5.2

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

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Step 5.2.1

Add $5$ to both sides of the equation.

$x = 2 + 5$

Step 5.2.2

Add $2$ and $5$ .

$x = 7$

Step 5.3

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

$x - 5 = - 2$

Step 5.4

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

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Step 5.4.1

Add $5$ to both sides of the equation.

$x = - 2 + 5$

Step 5.4.2

Add $- 2$ and $5$ .

$x = 3$

Step 5.5

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

$x = 7, 3$