Pre-Algebra Examples

$5 x + \frac{1}{10} = \frac{1}{20}$

Step 1

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

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Step 1.1

Subtract $\frac{1}{10}$ from both sides of the equation.

$5 x = \frac{1}{20} - \frac{1}{10}$

Step 1.2

To write $- \frac{1}{10}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$5 x = \frac{1}{20} - \frac{1}{10} \cdot \frac{2}{2}$

Step 1.3

Write each expression with a common denominator of $20$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.3.1

Multiply $\frac{1}{10}$ by $\frac{2}{2}$ .

$5 x = \frac{1}{20} - \frac{2}{10 \cdot 2}$

Step 1.3.2

Multiply $10$ by $2$ .

$5 x = \frac{1}{20} - \frac{2}{20}$

Step 1.4

Combine the numerators over the common denominator.

$5 x = \frac{1 - 2}{20}$

Step 1.5

Subtract $2$ from $1$ .

$5 x = \frac{- 1}{20}$

Step 1.6

Move the negative in front of the fraction.

$5 x = - \frac{1}{20}$

Step 2

Divide each term in $5 x = - \frac{1}{20}$ by $5$ and simplify.

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Step 2.1

Divide each term in $5 x = - \frac{1}{20}$ by $5$ .

$\frac{5 x}{5} = \frac{- \frac{1}{20}}{5}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $5$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{5 x}{5} = \frac{- \frac{1}{20}}{5}$

Step 2.2.1.2

Divide $x$ by $1$ .

$x = \frac{- \frac{1}{20}}{5}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Multiply the numerator by the reciprocal of the denominator.

$x = - \frac{1}{20} \cdot \frac{1}{5}$

Step 2.3.2

Multiply $- \frac{1}{20} \cdot \frac{1}{5}$ .

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Step 2.3.2.1

Multiply $\frac{1}{5}$ by $\frac{1}{20}$ .

$x = - \frac{1}{5 \cdot 20}$

Step 2.3.2.2

Multiply $5$ by $20$ .

$x = - \frac{1}{100}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{1}{100}$

Decimal Form:

$x = - 0.01$