Algebra Examples

$y = \frac{100 (0.02) + x (0.005)}{100 + x}$

Step 1

Simplify the numerator.

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Step 1.1

Factor $0.000025$ out of $100 (0.02) + x (0.005)$ .

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Step 1.1.1

Reorder $x$ and $0.005$ .

$y = \frac{100 (0.02) + 0.005 x}{100 + x}$

Step 1.1.2

Factor $0.000025$ out of $100 (0.02)$ .

$y = \frac{0.000025 (4000000 \cdot 0.02) + 0.005 x}{100 + x}$

Step 1.1.3

Factor $0.000025$ out of $0.005 x$ .

$y = \frac{0.000025 (4000000 \cdot 0.02) + 0.000025 (200 x)}{100 + x}$

Step 1.1.4

Factor $0.000025$ out of $0.000025 (4000000 \cdot 0.02) + 0.000025 (200 x)$ .

$y = \frac{0.000025 (4000000 \cdot 0.02 + 200 x)}{100 + x}$

Step 1.2

Factor $4$ out of $4000000 \cdot 0.02 + 200 x$ .

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Step 1.2.1

Factor $4$ out of $4000000 \cdot 0.02$ .

$y = \frac{0.000025 (4 (1000000 \cdot 0.02) + 200 x)}{100 + x}$

Step 1.2.2

Factor $4$ out of $200 x$ .

$y = \frac{0.000025 (4 (1000000 \cdot 0.02) + 4 (50 x))}{100 + x}$

Step 1.2.3

Factor $4$ out of $4 (1000000 \cdot 0.02) + 4 (50 x)$ .

$y = \frac{0.000025 (4 (1000000 \cdot 0.02 + 50 x))}{100 + x}$

Step 1.3

Multiply $1000000$ by $0.02$ .

$y = \frac{0.000025 (4 (20000 + 50 x))}{100 + x}$

Step 1.4

Factor $50$ out of $20000 + 50 x$ .

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Step 1.4.1

Factor $50$ out of $20000$ .

$y = \frac{0.000025 (4 (50 \cdot 400 + 50 x))}{100 + x}$

Step 1.4.2

Factor $50$ out of $50 \cdot 400 + 50 x$ .

$y = \frac{0.000025 (4 (50 (400 + x)))}{100 + x}$

$y = \frac{0.000025 (4 \cdot 50 (400 + x))}{100 + x}$

Step 1.5

Multiply $4$ by $50$ .

$y = \frac{0.000025 \cdot 200 (400 + x)}{100 + x}$

Step 1.6

Multiply $0.000025$ by $200$ .

$y = \frac{0.005 (400 + x)}{100 + x}$

Step 2

To rewrite as a function of $x$ , write the equation so that $y$ is by itself on one side of the equal sign and an expression involving only $x$ is on the other side.

$f (x) = \frac{0.005 (400 + x)}{100 + x}$