Algebra Examples

$7 - 2 | x - 6 | = - 13$

Step 1

Move all terms not containing $| x - 6 |$ to the right side of the equation.

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Step 1.1

Subtract $7$ from both sides of the equation.

$- 2 | x - 6 | = - 13 - 7$

Step 1.2

Subtract $7$ from $- 13$ .

$- 2 | x - 6 | = - 20$

Step 2

Divide each term in $- 2 | x - 6 | = - 20$ by $- 2$ and simplify.

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Step 2.1

Divide each term in $- 2 | x - 6 | = - 20$ by $- 2$ .

$\frac{- 2 | x - 6 |}{- 2} = \frac{- 20}{- 2}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $- 2$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{- 2 | x - 6 |}{- 2} = \frac{- 20}{- 2}$

Step 2.2.1.2

Divide $| x - 6 |$ by $1$ .

$| x - 6 | = \frac{- 20}{- 2}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide $- 20$ by $- 2$ .

$| x - 6 | = 10$

Step 3

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

$x - 6 = \pm 10$

Step 4

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

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Step 4.1

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

$x - 6 = 10$

Step 4.2

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

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Step 4.2.1

Add $6$ to both sides of the equation.

$x = 10 + 6$

Step 4.2.2

Add $10$ and $6$ .

$x = 16$

Step 4.3

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

$x - 6 = - 10$

Step 4.4

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

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Step 4.4.1

Add $6$ to both sides of the equation.

$x = - 10 + 6$

Step 4.4.2

Add $- 10$ and $6$ .

$x = - 4$

Step 4.5

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

$x = 16, - 4$