Finite Math Examples

$0.1 s \cdot 1 + 0.6 x \cdot 2 + 0.15 c \cdot 3 = 1$

Step 1

Simplify each term.

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Step 1.1

Multiply $0.1$ by $1$ .

$0.1 s + 0.6 x \cdot 2 + 0.15 c \cdot 3 = 1$

Step 1.2

Multiply $2$ by $0.6$ .

$0.1 s + 1.2 x + 0.15 c \cdot 3 = 1$

Step 1.3

Multiply $3$ by $0.15$ .

$0.1 s + 1.2 x + 0.45 c = 1$

Step 2

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

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Step 2.1

Subtract $1.2 x$ from both sides of the equation.

$0.1 s + 0.45 c = 1 - 1.2 x$

Step 2.2

Subtract $0.45 c$ from both sides of the equation.

$0.1 s = 1 - 1.2 x - 0.45 c$

Step 3

Divide each term in $0.1 s = 1 - 1.2 x - 0.45 c$ by $0.1$ and simplify.

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Step 3.1

Divide each term in $0.1 s = 1 - 1.2 x - 0.45 c$ by $0.1$ .

$\frac{0.1 s}{0.1} = \frac{1}{0.1} + \frac{- 1.2 x}{0.1} + \frac{- 0.45 c}{0.1}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $0.1$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{0.1 s}{0.1} = \frac{1}{0.1} + \frac{- 1.2 x}{0.1} + \frac{- 0.45 c}{0.1}$

Step 3.2.1.2

Divide $s$ by $1$ .

$s = \frac{1}{0.1} + \frac{- 1.2 x}{0.1} + \frac{- 0.45 c}{0.1}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Simplify each term.

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Step 3.3.1.1

Divide $1$ by $0.1$ .

$s = 10 + \frac{- 1.2 x}{0.1} + \frac{- 0.45 c}{0.1}$

Step 3.3.1.2

Move the negative in front of the fraction.

$s = 10 - \frac{1.2 x}{0.1} + \frac{- 0.45 c}{0.1}$

Step 3.3.1.3

Factor $1.2$ out of $1.2 x$ .

$s = 10 - \frac{1.2 (x)}{0.1} + \frac{- 0.45 c}{0.1}$

Step 3.3.1.4

Factor $0.1$ out of $0.1$ .

$s = 10 - \frac{1.2 (x)}{0.1 (1)} + \frac{- 0.45 c}{0.1}$

Step 3.3.1.5

Separate fractions.

$s = 10 - (\frac{1.2}{0.1} \cdot \frac{x}{1}) + \frac{- 0.45 c}{0.1}$

Step 3.3.1.6

Divide $1.2$ by $0.1$ .

$s = 10 - (12 \frac{x}{1}) + \frac{- 0.45 c}{0.1}$

Step 3.3.1.7

Divide $x$ by $1$ .

$s = 10 - (12 x) + \frac{- 0.45 c}{0.1}$

Step 3.3.1.8

Multiply $12$ by $- 1$ .

$s = 10 - 12 x + \frac{- 0.45 c}{0.1}$

Step 3.3.1.9

Move the negative in front of the fraction.

$s = 10 - 12 x - \frac{0.45 c}{0.1}$

Step 3.3.1.10

Factor $0.45$ out of $0.45 c$ .

$s = 10 - 12 x - \frac{0.45 (c)}{0.1}$

Step 3.3.1.11

Factor $0.1$ out of $0.1$ .

$s = 10 - 12 x - \frac{0.45 (c)}{0.1 (1)}$

Step 3.3.1.12

Separate fractions.

$s = 10 - 12 x - (\frac{0.45}{0.1} \cdot \frac{c}{1})$

Step 3.3.1.13

Divide $0.45$ by $0.1$ .

$s = 10 - 12 x - (4.5 \frac{c}{1})$

Step 3.3.1.14

Divide $c$ by $1$ .

$s = 10 - 12 x - (4.5 c)$

Step 3.3.1.15

Multiply $4.5$ by $- 1$ .

$s = 10 - 12 x - 4.5 c$