Algebra Examples

$3 - | x - 10 | = - 2$

Step 1

Move all terms not containing $| x - 10 |$ to the right side of the equation.

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Step 1.1

Subtract $3$ from both sides of the equation.

$- | x - 10 | = - 2 - 3$

Step 1.2

Subtract $3$ from $- 2$ .

$- | x - 10 | = - 5$

Step 2

Divide each term in $- | x - 10 | = - 5$ by $- 1$ and simplify.

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Step 2.1

Divide each term in $- | x - 10 | = - 5$ by $- 1$ .

$\frac{- | x - 10 |}{- 1} = \frac{- 5}{- 1}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Dividing two negative values results in a positive value.

$\frac{| x - 10 |}{1} = \frac{- 5}{- 1}$

Step 2.2.2

Divide $| x - 10 |$ by $1$ .

$| x - 10 | = \frac{- 5}{- 1}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide $- 5$ by $- 1$ .

$| x - 10 | = 5$

Step 3

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

$x - 10 = \pm 5$

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.

$x - 10 = 5$

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 $10$ to both sides of the equation.

$x = 5 + 10$

Step 4.2.2

Add $5$ and $10$ .

$x = 15$

Step 4.3

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

$x - 10 = - 5$

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 $10$ to both sides of the equation.

$x = - 5 + 10$

Step 4.4.2

Add $- 5$ and $10$ .

$x = 5$

Step 4.5

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

$x = 15, 5$