Pre-Algebra Examples

$y = 0.83 x + 39$

Step 1

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

Step 2

Change $0.83$ into a fraction.

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Step 2.1

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

$y = \frac{100 \cdot 0.83}{100} x + 39$

Step 2.2

Multiply $100$ by $0.83$ .

$y = \frac{83}{100} x + 39$

Step 2.3

Cancel the common factor of $83$ and $100$ .

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Step 2.3.1

Rewrite $83$ as $1 (83)$ .

$y = \frac{1 (83)}{100} x + 39$

Step 2.3.2

Cancel the common factors.

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Step 2.3.2.1

Rewrite $100$ as $1 (100)$ .

$y = \frac{1 \cdot 83}{1 \cdot 100} x + 39$

Step 2.3.2.2

Cancel the common factor.

$y = \frac{1 \cdot 83}{1 \cdot 100} x + 39$

Step 2.3.2.3

Rewrite the expression.

$y = \frac{83}{100} x + 39$

Step 3

Multiply both sides by $100$ .

$100 y = 100 (\frac{83}{100} x + 39)$

Step 4

Simplify the right side.

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Step 4.1

Simplify $100 (\frac{83}{100} x + 39)$ .

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Step 4.1.1

Combine $\frac{83}{100}$ and $x$ .

$100 y = 100 (\frac{83 x}{100} + 39)$

Step 4.1.2

Apply the distributive property.

$100 y = 100 \frac{83 x}{100} + 100 \cdot 39$

Step 4.1.3

Cancel the common factor of $100$ .

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Step 4.1.3.1

Cancel the common factor.

$100 y = 100 \frac{83 x}{100} + 100 \cdot 39$

Step 4.1.3.2

Rewrite the expression.

$100 y = 83 x + 100 \cdot 39$

Step 4.1.4

Multiply $100$ by $39$ .

$100 y = 83 x + 3900$

Step 5

Rewrite the equation.

$83 x + 3900 = 100 y$

Step 6

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

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Step 6.1

Subtract $100 y$ from both sides of the equation.

$83 x + 3900 - 100 y = 0$

Step 6.2

Move $3900$ .

$83 x - 100 y + 3900 = 0$

Step 7

Subtract $3900$ from both sides of the equation.

$83 x - 100 y = - 3900$

Step 8