Finite Math Examples

$\frac{2 (2 - 3 x)}{0.01} - 2.5 = \frac{0.02 - 2 x}{0.02} - 7.5$

Step 1

Move all the expressions to the left side of the equation.

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Step 1.1

Subtract $\frac{0.02 - 2 x}{0.02}$ from both sides of the equation.

$\frac{2 (2 - 3 x)}{0.01} - 2.5 - \frac{0.02 - 2 x}{0.02} = - 7.5$

Step 1.2

Add $7.5$ to both sides of the equation.

$\frac{2 (2 - 3 x)}{0.01} - 2.5 - \frac{0.02 - 2 x}{0.02} + 7.5 = 0$

Step 2

Simplify $\frac{2 (2 - 3 x)}{0.01} - 2.5 - \frac{0.02 - 2 x}{0.02} + 7.5$ .

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Step 2.1

Find the common denominator.

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Step 2.1.1

Multiply $\frac{2 (2 - 3 x)}{0.01}$ by $\frac{\frac{1}{0.01}}{\frac{1}{0.01}}$ .

$\frac{2 (2 - 3 x)}{0.01} \cdot \frac{\frac{1}{0.01}}{\frac{1}{0.01}} - 2.5 - \frac{0.02 - 2 x}{0.02} + 7.5 = 0$

Step 2.1.2

Multiply $\frac{2 (2 - 3 x)}{0.01}$ by $\frac{\frac{1}{0.01}}{\frac{1}{0.01}}$ .

$\frac{2 (2 - 3 x) \frac{1}{0.01}}{0.01 (\frac{1}{0.01})} - 2.5 - \frac{0.02 - 2 x}{0.02} + 7.5 = 0$

Step 2.1.3

Write $- 2.5$ as a fraction with denominator $1$ .

$\frac{2 (2 - 3 x) \frac{1}{0.01}}{0.01 (\frac{1}{0.01})} + \frac{- 2.5}{1} - \frac{0.02 - 2 x}{0.02} + 7.5 = 0$

Step 2.1.4

Multiply $\frac{- 2.5}{1}$ by $\frac{1}{1}$ .

$\frac{2 (2 - 3 x) \frac{1}{0.01}}{0.01 (\frac{1}{0.01})} + \frac{- 2.5}{1} \cdot \frac{1}{1} - \frac{0.02 - 2 x}{0.02} + 7.5 = 0$

Step 2.1.5

Multiply $\frac{- 2.5}{1}$ by $\frac{1}{1}$ .

$\frac{2 (2 - 3 x) \frac{1}{0.01}}{0.01 (\frac{1}{0.01})} + \frac{- 2.5}{1} - \frac{0.02 - 2 x}{0.02} + 7.5 = 0$

Step 2.1.6

Multiply $\frac{0.02 - 2 x}{0.02}$ by $\frac{\frac{1}{0.02}}{\frac{1}{0.02}}$ .

$\frac{2 (2 - 3 x) \frac{1}{0.01}}{0.01 (\frac{1}{0.01})} + \frac{- 2.5}{1} - (\frac{0.02 - 2 x}{0.02} \cdot \frac{\frac{1}{0.02}}{\frac{1}{0.02}}) + 7.5 = 0$

Step 2.1.7

Multiply $\frac{0.02 - 2 x}{0.02}$ by $\frac{\frac{1}{0.02}}{\frac{1}{0.02}}$ .

$\frac{2 (2 - 3 x) \frac{1}{0.01}}{0.01 (\frac{1}{0.01})} + \frac{- 2.5}{1} - \frac{(0.02 - 2 x) \frac{1}{0.02}}{0.02 (\frac{1}{0.02})} + 7.5 = 0$

Step 2.1.8

Write $7.5$ as a fraction with denominator $1$ .

$\frac{2 (2 - 3 x) \frac{1}{0.01}}{0.01 (\frac{1}{0.01})} + \frac{- 2.5}{1} - \frac{(0.02 - 2 x) \frac{1}{0.02}}{0.02 (\frac{1}{0.02})} + \frac{7.5}{1} = 0$

Step 2.1.9

Multiply $\frac{7.5}{1}$ by $\frac{1}{1}$ .

$\frac{2 (2 - 3 x) \frac{1}{0.01}}{0.01 (\frac{1}{0.01})} + \frac{- 2.5}{1} - \frac{(0.02 - 2 x) \frac{1}{0.02}}{0.02 (\frac{1}{0.02})} + \frac{7.5}{1} \cdot \frac{1}{1} = 0$

Step 2.1.10

Multiply $\frac{7.5}{1}$ by $\frac{1}{1}$ .

$\frac{2 (2 - 3 x) \frac{1}{0.01}}{0.01 (\frac{1}{0.01})} + \frac{- 2.5}{1} - \frac{(0.02 - 2 x) \frac{1}{0.02}}{0.02 (\frac{1}{0.02})} + \frac{7.5}{1} = 0$

Step 2.1.11

Combine $0.01$ and $\frac{1}{0.01}$ .

$\frac{2 (2 - 3 x) \frac{1}{0.01}}{\frac{0.01}{0.01}} + \frac{- 2.5}{1} - \frac{(0.02 - 2 x) \frac{1}{0.02}}{0.02 (\frac{1}{0.02})} + \frac{7.5}{1} = 0$

Step 2.1.12

Combine $0.02$ and $\frac{1}{0.02}$ .

$\frac{2 (2 - 3 x) \frac{1}{0.01}}{\frac{0.01}{0.01}} + \frac{- 2.5}{1} - \frac{(0.02 - 2 x) \frac{1}{0.02}}{\frac{0.02}{0.02}} + \frac{7.5}{1} = 0$

Step 2.2

Combine the numerators over the common denominator.

$\frac{2 (2 - 3 x) \frac{1}{0.01}}{\frac{0.01}{0.01}} + \frac{- 2.5 + 7.5}{1} + \frac{- (0.02 - 2 x) \frac{1}{0.02}}{\frac{0.02}{0.02}} = 0$

Step 2.3

Add $- 2.5$ and $7.5$ .

$\frac{2 (2 - 3 x) \frac{1}{0.01}}{\frac{0.01}{0.01}} + \frac{5}{1} + \frac{- (0.02 - 2 x) \frac{1}{0.02}}{\frac{0.02}{0.02}} = 0$

Step 2.4

Combine the numerators over the common denominator.

$\frac{2 (2 - 3 x) \frac{1}{0.01} + 5 - (0.02 - 2 x) \frac{1}{0.02}}{\frac{0.01}{0.01}} = 0$

Step 2.5

Cancel the common factor of $0.01$ .

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Step 2.5.1

Cancel the common factor.

$\frac{2 (2 - 3 x) \frac{1}{0.01} + 5 - (0.02 - 2 x) \frac{1}{0.02}}{\frac{0.01}{0.01}} = 0$

Step 2.5.2

Rewrite the expression.

$\frac{2 (2 - 3 x) \frac{1}{0.01} + 5 - (0.02 - 2 x) \frac{1}{0.02}}{1} = 0$

Step 2.6

Divide $2 (2 - 3 x) \frac{1}{0.01} + 5 - (0.02 - 2 x) \frac{1}{0.02}$ by $1$ .

$2 (2 - 3 x) \frac{1}{0.01} + 5 - (0.02 - 2 x) \frac{1}{0.02} = 0$

Step 2.7

Simplify each term.

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Step 2.7.1

Cancel the common factor of $0.01$ .

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Step 2.7.1.1

Factor $0.01$ out of $2 (2 - 3 x)$ .

$0.01 (200 (2 - 3 x)) \frac{1}{0.01} + 5 - (0.02 - 2 x) \frac{1}{0.02} = 0$

Step 2.7.1.2

Cancel the common factor.

$0.01 (200 (2 - 3 x)) \frac{1}{0.01} + 5 - (0.02 - 2 x) \frac{1}{0.02} = 0$

Step 2.7.1.3

Rewrite the expression.

$200 (2 - 3 x) + 5 - (0.02 - 2 x) \frac{1}{0.02} = 0$

Step 2.7.2

Apply the distributive property.

$200 \cdot 2 + 200 (- 3 x) + 5 - (0.02 - 2 x) \frac{1}{0.02} = 0$

Step 2.7.3

Multiply $200$ by $2$ .

$400 + 200 (- 3 x) + 5 - (0.02 - 2 x) \frac{1}{0.02} = 0$

Step 2.7.4

Multiply $- 3$ by $200$ .

$400 - 600 x + 5 - (0.02 - 2 x) \frac{1}{0.02} = 0$

Step 2.7.5

Cancel the common factor of $0.02$ .

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Step 2.7.5.1

Factor $0.02$ out of $- (0.02 - 2 x)$ .

$400 - 600 x + 5 + 0.02 (- 50 (0.02 - 2 x)) \frac{1}{0.02} = 0$

Step 2.7.5.2

Cancel the common factor.

$400 - 600 x + 5 + 0.02 (- 50 (0.02 - 2 x)) \frac{1}{0.02} = 0$

Step 2.7.5.3

Rewrite the expression.

$400 - 600 x + 5 - 50 (0.02 - 2 x) = 0$

Step 2.7.6

Apply the distributive property.

$400 - 600 x + 5 - 50 \cdot 0.02 - 50 (- 2 x) = 0$

Step 2.7.7

Multiply $- 50$ by $0.02$ .

$400 - 600 x + 5 - 1 - 50 (- 2 x) = 0$

Step 2.7.8

Multiply $- 2$ by $- 50$ .

$400 - 600 x + 5 - 1 + 100 x = 0$

Step 2.8

Add $400$ and $5$ .

$- 600 x + 405 - 1 + 100 x = 0$

Step 2.9

Add $- 600 x$ and $100 x$ .

$- 500 x + 405 - 1 = 0$

Step 2.10

Subtract $1$ from $405$ .

$- 500 x + 404 = 0$

Step 3

Factor $- 4$ out of $- 500 x + 404$ .

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Step 3.1

Factor $- 4$ out of $- 500 x$ .

$- 4 (125 x) + 404 = 0$

Step 3.2

Factor $- 4$ out of $404$ .

$- 4 (125 x) - 4 \cdot - 101 = 0$

Step 3.3

Factor $- 4$ out of $- 4 (125 x) - 4 (- 101)$ .

$- 4 (125 x - 101) = 0$