Write in Standard Form -0.08x=1.24y-3.12

$- 0.08 x = 1.24 y - 3.12$

Step 1

The standard form of a linear equation is $A x + B y = C$ .

Step 2

Change $- 0.08$ into a fraction.

Multiply by $\frac{100}{100}$ to remove the decimal.

$\frac{100 \cdot - 0.08}{100} x = 1.24 y - 3.12$

Multiply $100$ by $- 0.08$ .

$\frac{- 8}{100} x = 1.24 y - 3.12$

Move the negative in front of the fraction.

$- \frac{8}{100} x = 1.24 y - 3.12$

Cancel the common factor of $8$ and $100$ .

Factor $4$ out of $8$ .

$- \frac{4 (2)}{100} x = 1.24 y - 3.12$

Cancel the common factors.

Factor $4$ out of $100$ .

$- \frac{4 \cdot 2}{4 \cdot 25} x = 1.24 y - 3.12$

Cancel the common factor.

$- \frac{4 \cdot 2}{4 \cdot 25} x = 1.24 y - 3.12$

Rewrite the expression.

$- \frac{2}{25} x = 1.24 y - 3.12$

Step 3

Change $1.24$ into a fraction.

Multiply by $\frac{100}{100}$ to remove the decimal.

$- \frac{2}{25} x = \frac{100 \cdot 1.24}{100} y - 3.12$

Multiply $100$ by $1.24$ .

$- \frac{2}{25} x = \frac{124}{100} y - 3.12$

Cancel the common factor of $124$ and $100$ .

Factor $4$ out of $124$ .

$- \frac{2}{25} x = \frac{4 (31)}{100} y - 3.12$

Cancel the common factors.

Factor $4$ out of $100$ .

$- \frac{2}{25} x = \frac{4 \cdot 31}{4 \cdot 25} y - 3.12$

Cancel the common factor.

$- \frac{2}{25} x = \frac{4 \cdot 31}{4 \cdot 25} y - 3.12$

Rewrite the expression.

$- \frac{2}{25} x = \frac{31}{25} y - 3.12$

Step 4

Change $- 3.12$ into a fraction.

Multiply by $\frac{100}{100}$ to remove the decimal.

$- \frac{2}{25} x = \frac{31}{25} y + \frac{100 \cdot - 3.12}{100}$

Multiply $100$ by $- 3.12$ .

$- \frac{2}{25} x = \frac{31}{25} y + \frac{- 312}{100}$

Move the negative in front of the fraction.

$- \frac{2}{25} x = \frac{31}{25} y - \frac{312}{100}$

Cancel the common factor of $312$ and $100$ .

Factor $4$ out of $312$ .

$- \frac{2}{25} x = \frac{31}{25} y - \frac{4 (78)}{100}$

Cancel the common factors.

Factor $4$ out of $100$ .

$- \frac{2}{25} x = \frac{31}{25} y - \frac{4 \cdot 78}{4 \cdot 25}$

Cancel the common factor.

$- \frac{2}{25} x = \frac{31}{25} y - \frac{4 \cdot 78}{4 \cdot 25}$

Rewrite the expression.

$- \frac{2}{25} x = \frac{31}{25} y - \frac{78}{25}$

Step 5

Find the LCD of $\frac{2}{25}$ , $\frac{31}{25}$ , and $\frac{78}{25}$ .

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$25, 25, 25$

Since $25, 25, 25$ contain both numbers and variables, there are two steps to find the LCM. Find LCM for the numeric part $25, 25, 25$ then find LCM for the variable part .

The LCM is the smallest positive number that all of the numbers divide into evenly.

1. List the prime factors of each number.

2. Multiply each factor the greatest number of times it occurs in either number.

$25$ has factors of $5$ and $5$ .

$5 \cdot 5$

Multiply $5$ by $5$ .

$25$

Step 6

Multiply both sides by $25$ .

$25 (- \frac{2}{25} x) = 25 (\frac{31}{25} y - \frac{78}{25})$

Step 7

Simplify the left side.

Simplify $25 (- \frac{2}{25} x)$ .

Combine $x$ and $\frac{2}{25}$ .

$25 (- \frac{x \cdot 2}{25}) = 25 (\frac{31}{25} y - \frac{78}{25})$

Cancel the common factor of $25$ .

Move the leading negative in $- \frac{x \cdot 2}{25}$ into the numerator.

$25 \frac{- x \cdot 2}{25} = 25 (\frac{31}{25} y - \frac{78}{25})$

Cancel the common factor.

$25 \frac{- x \cdot 2}{25} = 25 (\frac{31}{25} y - \frac{78}{25})$

Rewrite the expression.

$- x \cdot 2 = 25 (\frac{31}{25} y - \frac{78}{25})$

Multiply $2$ by $- 1$ .

$- 2 x = 25 (\frac{31}{25} y - \frac{78}{25})$

Step 8

Simplify the right side.

Simplify $25 (\frac{31}{25} y - \frac{78}{25})$ .

Combine $\frac{31}{25}$ and $y$ .

$- 2 x = 25 (\frac{31 y}{25} - \frac{78}{25})$

Apply the distributive property.

$- 2 x = 25 \frac{31 y}{25} + 25 (- \frac{78}{25})$

Cancel the common factor of $25$ .

Cancel the common factor.

$- 2 x = 25 \frac{31 y}{25} + 25 (- \frac{78}{25})$

Rewrite the expression.

$- 2 x = 31 y + 25 (- \frac{78}{25})$

Cancel the common factor of $25$ .

Move the leading negative in $- \frac{78}{25}$ into the numerator.

$- 2 x = 31 y + 25 (\frac{- 78}{25})$

Cancel the common factor.

$- 2 x = 31 y + 25 (\frac{- 78}{25})$

Rewrite the expression.

$- 2 x = 31 y - 78$

Step 9

Rewrite the equation.

$31 y - 78 = - 2 x$

Step 10

Move all terms containing variables to the left side of the equation.

Add $2 x$ to both sides of the equation.

$31 y - 78 + 2 x = 0$

Move $- 78$ .

$31 y + 2 x - 78 = 0$

Reorder $31 y$ and $2 x$ .

$2 x + 31 y - 78 = 0$

Step 11

Add $78$ to both sides of the equation.

$2 x + 31 y = 78$

Step 12

Write in Standard Form -0.08x=1.24y-3.12

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