Pre-Algebra Examples

$| \frac{2}{25} + 5 x | = \frac{1}{10}$

Step 1

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

$\frac{2}{25} + 5 x = \pm \frac{1}{10}$

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.

$\frac{2}{25} + 5 x = \frac{1}{10}$

Step 2.2

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

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Step 2.2.1

Subtract $\frac{2}{25}$ from both sides of the equation.

$5 x = \frac{1}{10} - \frac{2}{25}$

Step 2.2.2

To write $\frac{1}{10}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$5 x = \frac{1}{10} \cdot \frac{5}{5} - \frac{2}{25}$

Step 2.2.3

To write $- \frac{2}{25}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$5 x = \frac{1}{10} \cdot \frac{5}{5} - \frac{2}{25} \cdot \frac{2}{2}$

Step 2.2.4

Write each expression with a common denominator of $50$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.2.4.1

Multiply $\frac{1}{10}$ by $\frac{5}{5}$ .

$5 x = \frac{5}{10 \cdot 5} - \frac{2}{25} \cdot \frac{2}{2}$

Step 2.2.4.2

Multiply $10$ by $5$ .

$5 x = \frac{5}{50} - \frac{2}{25} \cdot \frac{2}{2}$

Step 2.2.4.3

Multiply $\frac{2}{25}$ by $\frac{2}{2}$ .

$5 x = \frac{5}{50} - \frac{2 \cdot 2}{25 \cdot 2}$

Step 2.2.4.4

Multiply $25$ by $2$ .

$5 x = \frac{5}{50} - \frac{2 \cdot 2}{50}$

Step 2.2.5

Combine the numerators over the common denominator.

$5 x = \frac{5 - 2 \cdot 2}{50}$

Step 2.2.6

Simplify the numerator.

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Step 2.2.6.1

Multiply $- 2$ by $2$ .

$5 x = \frac{5 - 4}{50}$

Step 2.2.6.2

Subtract $4$ from $5$ .

$5 x = \frac{1}{50}$

Step 2.3

Divide each term in $5 x = \frac{1}{50}$ by $5$ and simplify.

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Step 2.3.1

Divide each term in $5 x = \frac{1}{50}$ by $5$ .

$\frac{5 x}{5} = \frac{\frac{1}{50}}{5}$

Step 2.3.2

Simplify the left side.

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Step 2.3.2.1

Cancel the common factor of $5$ .

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Step 2.3.2.1.1

Cancel the common factor.

$\frac{5 x}{5} = \frac{\frac{1}{50}}{5}$

Step 2.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{\frac{1}{50}}{5}$

Step 2.3.3

Simplify the right side.

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Step 2.3.3.1

Multiply the numerator by the reciprocal of the denominator.

$x = \frac{1}{50} \cdot \frac{1}{5}$

Step 2.3.3.2

Multiply $\frac{1}{50} \cdot \frac{1}{5}$ .

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Step 2.3.3.2.1

Multiply $\frac{1}{50}$ by $\frac{1}{5}$ .

$x = \frac{1}{50 \cdot 5}$

Step 2.3.3.2.2

Multiply $50$ by $5$ .

$x = \frac{1}{250}$

Step 2.4

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

$\frac{2}{25} + 5 x = - \frac{1}{10}$

Step 2.5

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

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Step 2.5.1

Subtract $\frac{2}{25}$ from both sides of the equation.

$5 x = - \frac{1}{10} - \frac{2}{25}$

Step 2.5.2

To write $- \frac{1}{10}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$5 x = - \frac{1}{10} \cdot \frac{5}{5} - \frac{2}{25}$

Step 2.5.3

To write $- \frac{2}{25}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$5 x = - \frac{1}{10} \cdot \frac{5}{5} - \frac{2}{25} \cdot \frac{2}{2}$

Step 2.5.4

Write each expression with a common denominator of $50$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.5.4.1

Multiply $\frac{1}{10}$ by $\frac{5}{5}$ .

$5 x = - \frac{5}{10 \cdot 5} - \frac{2}{25} \cdot \frac{2}{2}$

Step 2.5.4.2

Multiply $10$ by $5$ .

$5 x = - \frac{5}{50} - \frac{2}{25} \cdot \frac{2}{2}$

Step 2.5.4.3

Multiply $\frac{2}{25}$ by $\frac{2}{2}$ .

$5 x = - \frac{5}{50} - \frac{2 \cdot 2}{25 \cdot 2}$

Step 2.5.4.4

Multiply $25$ by $2$ .

$5 x = - \frac{5}{50} - \frac{2 \cdot 2}{50}$

Step 2.5.5

Combine the numerators over the common denominator.

$5 x = \frac{- 5 - 2 \cdot 2}{50}$

Step 2.5.6

Simplify the numerator.

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Step 2.5.6.1

Multiply $- 2$ by $2$ .

$5 x = \frac{- 5 - 4}{50}$

Step 2.5.6.2

Subtract $4$ from $- 5$ .

$5 x = \frac{- 9}{50}$

Step 2.5.7

Move the negative in front of the fraction.

$5 x = - \frac{9}{50}$

Step 2.6

Divide each term in $5 x = - \frac{9}{50}$ by $5$ and simplify.

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Step 2.6.1

Divide each term in $5 x = - \frac{9}{50}$ by $5$ .

$\frac{5 x}{5} = \frac{- \frac{9}{50}}{5}$

Step 2.6.2

Simplify the left side.

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Step 2.6.2.1

Cancel the common factor of $5$ .

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Step 2.6.2.1.1

Cancel the common factor.

$\frac{5 x}{5} = \frac{- \frac{9}{50}}{5}$

Step 2.6.2.1.2

Divide $x$ by $1$ .

$x = \frac{- \frac{9}{50}}{5}$

Step 2.6.3

Simplify the right side.

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Step 2.6.3.1

Multiply the numerator by the reciprocal of the denominator.

$x = - \frac{9}{50} \cdot \frac{1}{5}$

Step 2.6.3.2

Multiply $- \frac{9}{50} \cdot \frac{1}{5}$ .

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Step 2.6.3.2.1

Multiply $\frac{1}{5}$ by $\frac{9}{50}$ .

$x = - \frac{9}{5 \cdot 50}$

Step 2.6.3.2.2

Multiply $5$ by $50$ .

$x = - \frac{9}{250}$

Step 2.7

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

$x = \frac{1}{250}, - \frac{9}{250}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = \frac{1}{250}, - \frac{9}{250}$

Decimal Form:

$x = 0.004, - 0.036$