Algebra Examples

0.01 x + 0.001 = \frac{1}{100} (x + 10)

$0.01 x + 0.001 = \frac{1}{100} (x + 10)$

Step 1

Simplify

\frac{1}{100} \cdot (x + 10)

$\frac{1}{100} \cdot (x + 10)$ .

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Step 1.1

Rewrite.

0.01 x + 0.001 = 0 + 0 + \frac{1}{100} \cdot (x + 10)

$0.01 x + 0.001 = 0 + 0 + \frac{1}{100} \cdot (x + 10)$

Step 1.2

Simplify by adding zeros.

0.01 x + 0.001 = \frac{1}{100} \cdot (x + 10)

$0.01 x + 0.001 = \frac{1}{100} \cdot (x + 10)$

Step 1.3

Apply the distributive property.

0.01 x + 0.001 = \frac{1}{100} x + \frac{1}{100} \cdot 10

$0.01 x + 0.001 = \frac{1}{100} x + \frac{1}{100} \cdot 10$

Step 1.4

Combine

\frac{1}{100}

$\frac{1}{100}$ and

x

$x$ .

0.01 x + 0.001 = \frac{x}{100} + \frac{1}{100} \cdot 10

$0.01 x + 0.001 = \frac{x}{100} + \frac{1}{100} \cdot 10$

Step 1.5

Cancel the common factor of

10

$10$ .

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Step 1.5.1

Factor

10

$10$ out of

100

$100$ .

0.01 x + 0.001 = \frac{x}{100} + \frac{1}{10 (10)} \cdot 10

$0.01 x + 0.001 = \frac{x}{100} + \frac{1}{10 (10)} \cdot 10$

Step 1.5.2

Cancel the common factor.

0.01 x + 0.001 = \frac{x}{100} + \frac{1}{10 \cdot 10} \cdot 10

$0.01 x + 0.001 = \frac{x}{100} + \frac{1}{10 \cdot 10} \cdot 10$

Step 1.5.3

Rewrite the expression.

0.01 x + 0.001 = \frac{x}{100} + \frac{1}{10}

$0.01 x + 0.001 = \frac{x}{100} + \frac{1}{10}$

0.01 x + 0.001 = \frac{x}{100} + \frac{1}{10}

$0.01 x + 0.001 = \frac{x}{100} + \frac{1}{10}$

0.01 x + 0.001 = \frac{x}{100} + \frac{1}{10}

$0.01 x + 0.001 = \frac{x}{100} + \frac{1}{10}$

Step 2

Move all terms containing

x

$x$ to the left side of the equation.

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Step 2.1

Subtract

\frac{x}{100}

$\frac{x}{100}$ from both sides of the equation.

0.01 x + 0.001 - \frac{x}{100} = \frac{1}{10}

$0.01 x + 0.001 - \frac{x}{100} = \frac{1}{10}$

Step 2.2

To write

0.01 x

$0.01 x$ as a fraction with a common denominator, multiply by

\frac{100}{100}

$\frac{100}{100}$ .

0.01 x \cdot \frac{100}{100} - \frac{x}{100} + 0.001 = \frac{1}{10}

$0.01 x \cdot \frac{100}{100} - \frac{x}{100} + 0.001 = \frac{1}{10}$

Step 2.3

Combine

0.01 x

$0.01 x$ and

\frac{100}{100}

$\frac{100}{100}$ .

\frac{0.01 x \cdot 100}{100} - \frac{x}{100} + 0.001 = \frac{1}{10}

$\frac{0.01 x \cdot 100}{100} - \frac{x}{100} + 0.001 = \frac{1}{10}$

Step 2.4

Combine the numerators over the common denominator.

\frac{0.01 x \cdot 100 - x}{100} + 0.001 = \frac{1}{10}

$\frac{0.01 x \cdot 100 - x}{100} + 0.001 = \frac{1}{10}$

Step 2.5

Simplify each term.

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Step 2.5.1

Simplify the numerator.

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Step 2.5.1.1

Factor

0.01 x

$0.01 x$ out of

0.01 x \cdot 100 - x

$0.01 x \cdot 100 - x$ .

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Step 2.5.1.1.1

Move

x

$x$ .

\frac{0.01 \cdot 100 x - x}{100} + 0.001 = \frac{1}{10}

$\frac{0.01 \cdot 100 x - x}{100} + 0.001 = \frac{1}{10}$

Step 2.5.1.1.2

Factor

0.01 x

$0.01 x$ out of

0.01 \cdot 100 x

$0.01 \cdot 100 x$ .

\frac{0.01 x (100) - x}{100} + 0.001 = \frac{1}{10}

$\frac{0.01 x (100) - x}{100} + 0.001 = \frac{1}{10}$

Step 2.5.1.1.3

Factor

0.01 x

$0.01 x$ out of

- x

$- x$ .

\frac{0.01 x (100) + 0.01 x (- 100)}{100} + 0.001 = \frac{1}{10}

$\frac{0.01 x (100) + 0.01 x (- 100)}{100} + 0.001 = \frac{1}{10}$

Step 2.5.1.1.4

Factor

0.01 x

$0.01 x$ out of

0.01 x (100) + 0.01 x (- 100)

$0.01 x (100) + 0.01 x (- 100)$ .

\frac{0.01 x (100 - 100)}{100} + 0.001 = \frac{1}{10}

$\frac{0.01 x (100 - 100)}{100} + 0.001 = \frac{1}{10}$

\frac{0.01 x (100 - 100)}{100} + 0.001 = \frac{1}{10}

$\frac{0.01 x (100 - 100)}{100} + 0.001 = \frac{1}{10}$

Step 2.5.1.2

Combine exponents.

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Step 2.5.1.2.1

Multiply

100 - 100

$100 - 100$ by

0.01

$0.01$ .

\frac{0 x}{100} + 0.001 = \frac{1}{10}

$\frac{0 x}{100} + 0.001 = \frac{1}{10}$

Step 2.5.1.2.2

Multiply

0

$0$ by

x

$x$ .

\frac{0}{100} + 0.001 = \frac{1}{10}

$\frac{0}{100} + 0.001 = \frac{1}{10}$

\frac{0}{100} + 0.001 = \frac{1}{10}

$\frac{0}{100} + 0.001 = \frac{1}{10}$

\frac{0}{100} + 0.001 = \frac{1}{10}

$\frac{0}{100} + 0.001 = \frac{1}{10}$

Step 2.5.2

Divide

0

$0$ by

100

$100$ .

0 + 0.001 = \frac{1}{10}

$0 + 0.001 = \frac{1}{10}$

0 + 0.001 = \frac{1}{10}

$0 + 0.001 = \frac{1}{10}$

Step 2.6

Add

0

$0$ and

0.001

$0.001$ .

0.001 = \frac{1}{10}

$0.001 = \frac{1}{10}$

0.001 = \frac{1}{10}

$0.001 = \frac{1}{10}$

Step 3

Since

0.001 \neq \frac{1}{10}

$0.001 \neq \frac{1}{10}$ , there are no solutions.

No solution