Finite Math Examples

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

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

Step 1

Simplify each term.

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Step 1.1

Multiply

0.1

$0.1$ by

1

$1$ .

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

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

Step 1.2

Multiply

2

$2$ by

0.6

$0.6$ .

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

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

Step 1.3

Multiply

3

$3$ by

0.15

$0.15$ .

0.1 s + 1.2 x + 0.45 c = 1

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

0.1 s + 1.2 x + 0.45 c = 1

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

Step 2

Move all terms not containing

s

$s$ to the right side of the equation.

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Step 2.1

Subtract

1.2 x

$1.2 x$ from both sides of the equation.

0.1 s + 0.45 c = 1 - 1.2 x

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

Step 2.2

Subtract

0.45 c

$0.45 c$ from both sides of the equation.

0.1 s = 1 - 1.2 x - 0.45 c

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

0.1 s = 1 - 1.2 x - 0.45 c

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

Step 3

Divide each term in

0.1 s = 1 - 1.2 x - 0.45 c

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

0.1

$0.1$ and simplify.

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Step 3.1

Divide each term in

0.1 s = 1 - 1.2 x - 0.45 c

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

0.1

$0.1$ .

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

$0.1$ .

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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}

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

Step 3.2.1.2

Divide

s

$s$ by

1

$1$ .

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

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

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

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

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

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

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

$1$ by

0.1

$0.1$ .

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

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

Step 3.3.1.3

Factor

1.2

$1.2$ out of

1.2 x

$1.2 x$ .

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

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

Step 3.3.1.4

Factor

0.1

$0.1$ out of

0.1

$0.1$ .

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

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

Step 3.3.1.6

Divide

1.2

$1.2$ by

0.1

$0.1$ .

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

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

Step 3.3.1.7

Divide

x

$x$ by

1

$1$ .

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

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

Step 3.3.1.8

Multiply

12

$12$ by

- 1

$- 1$ .

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

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

Step 3.3.1.9

Move the negative in front of the fraction.

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

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

Step 3.3.1.10

Factor

0.45

$0.45$ out of

0.45 c

$0.45 c$ .

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

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

Step 3.3.1.11

Factor

0.1

$0.1$ out of

0.1

$0.1$ .

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

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

Step 3.3.1.13

Divide

0.45

$0.45$ by

0.1

$0.1$ .

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

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

Step 3.3.1.14

Divide

c

$c$ by

1

$1$ .

s = 10 - 12 x - (4.5 c)

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

Step 3.3.1.15

Multiply

4.5

$4.5$ by

- 1

$- 1$ .

s = 10 - 12 x - 4.5 c

$s = 10 - 12 x - 4.5 c$

s = 10 - 12 x - 4.5 c

$s = 10 - 12 x - 4.5 c$

s = 10 - 12 x - 4.5 c

$s = 10 - 12 x - 4.5 c$

s = 10 - 12 x - 4.5 c

$s = 10 - 12 x - 4.5 c$