Finite Math Examples

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

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

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

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.