Algebra Examples

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

Step 1

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

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Step 1.1

Rewrite.

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

Step 1.2

Simplify by adding zeros.

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

Step 1.3

Apply the distributive property.

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

Step 1.4

Combine $\frac{1}{100}$ and $x$ .

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

Step 1.5

Cancel the common factor of $10$ .

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Step 1.5.1

Factor $10$ out of $100$ .

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

Step 1.5.2

Cancel the common factor.

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

Step 1.5.3

Rewrite the expression.

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

Step 2

Move all terms containing $x$ to the left side of the equation.

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Step 2.1

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

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

Step 2.2

To write $0.01 x$ as a fraction with a common denominator, multiply by $\frac{100}{100}$ .

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

Step 2.3

Combine $0.01 x$ and $\frac{100}{100}$ .

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

Step 2.4

Combine the numerators over the common denominator.

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

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 $0.01 x$ out of $0.01 x \cdot 100 - x$ .

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Step 2.5.1.1.1

Move $x$ .

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

Step 2.5.1.1.2

Factor $0.01 x$ out of $0.01 \cdot 100 x$ .

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

Step 2.5.1.1.3

Factor $0.01 x$ out of $- x$ .

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

Step 2.5.1.1.4

Factor $0.01 x$ out of $0.01 x (100) + 0.01 x (- 100)$ .

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

Step 2.5.1.2

Combine exponents.

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Step 2.5.1.2.1

Multiply $100 - 100$ by $0.01$ .

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

Step 2.5.1.2.2

Multiply $0$ by $x$ .

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

Step 2.5.2

Divide $0$ by $100$ .

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

Step 2.6

Add $0$ and $0.001$ .

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

Step 3

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

No solution