Algebra Examples

$10 y = 12 x + 0.7$

Step 1

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

Step 2

Change $0.7$ into a fraction.

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Step 2.1

Multiply by $\frac{10}{10}$ to remove the decimal.

$10 y = 12 x + \frac{10 \cdot 0.7}{10}$

Step 2.2

Multiply $10$ by $0.7$ .

$10 y = 12 x + \frac{7}{10}$

Step 2.3

Cancel the common factor of $7$ and $10$ .

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Step 2.3.1

Rewrite $7$ as $1 (7)$ .

$10 y = 12 x + \frac{1 (7)}{10}$

Step 2.3.2

Cancel the common factors.

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Step 2.3.2.1

Rewrite $10$ as $1 (10)$ .

$10 y = 12 x + \frac{1 \cdot 7}{1 \cdot 10}$

Step 2.3.2.2

Cancel the common factor.

$10 y = 12 x + \frac{1 \cdot 7}{1 \cdot 10}$

Step 2.3.2.3

Rewrite the expression.

$10 y = 12 x + \frac{7}{10}$

Step 3

Multiply both sides by $10$ .

$10 (10 y) = 10 (12 x + \frac{7}{10})$

Step 4

Simplify the left side.

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Step 4.1

Multiply $10$ by $10$ .

$100 y = 10 (12 x + \frac{7}{10})$

Step 5

Simplify the right side.

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Step 5.1

Simplify $10 (12 x + \frac{7}{10})$ .

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Step 5.1.1

Apply the distributive property.

$100 y = 10 (12 x) + 10 (\frac{7}{10})$

Step 5.1.2

Multiply $12$ by $10$ .

$100 y = 120 x + 10 (\frac{7}{10})$

Step 5.1.3

Cancel the common factor of $10$ .

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Step 5.1.3.1

Cancel the common factor.

$100 y = 120 x + 10 (\frac{7}{10})$

Step 5.1.3.2

Rewrite the expression.

$100 y = 120 x + 7$

Step 6

Rewrite the equation.

$120 x + 7 = 100 y$

Step 7

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

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Step 7.1

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

$120 x + 7 - 100 y = 0$

Step 7.2

Move $7$ .

$120 x - 100 y + 7 = 0$

Step 8

Subtract $7$ from both sides of the equation.

$120 x - 100 y = - 7$

Step 9