Pre-Algebra Examples

$y - 2 = - 0.4 (x - 8)$

Step 1

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

Step 2

Change $- 0.4$ into a fraction.

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Step 2.1

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

$y - 2 = \frac{10 \cdot - 0.4}{10} (x - 8)$

Step 2.2

Multiply $10$ by $- 0.4$ .

$y - 2 = \frac{- 4}{10} (x - 8)$

Step 2.3

Move the negative in front of the fraction.

$y - 2 = - \frac{4}{10} (x - 8)$

Step 2.4

Cancel the common factor of $4$ and $10$ .

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Step 2.4.1

Factor $2$ out of $4$ .

$y - 2 = - \frac{2 (2)}{10} (x - 8)$

Step 2.4.2

Cancel the common factors.

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Step 2.4.2.1

Factor $2$ out of $10$ .

$y - 2 = - \frac{2 \cdot 2}{2 \cdot 5} (x - 8)$

Step 2.4.2.2

Cancel the common factor.

$y - 2 = - \frac{2 \cdot 2}{2 \cdot 5} (x - 8)$

Step 2.4.2.3

Rewrite the expression.

$y - 2 = - \frac{2}{5} (x - 8)$

Step 3

Multiply both sides by $5$ .

$5 (y - 2) = 5 (- \frac{2}{5} (x - 8))$

Step 4

Simplify the left side.

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Step 4.1

Simplify $5 (y - 2)$ .

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Step 4.1.1

Apply the distributive property.

$5 y + 5 \cdot - 2 = 5 (- \frac{2}{5} (x - 8))$

Step 4.1.2

Multiply $5$ by $- 2$ .

$5 y - 10 = 5 (- \frac{2}{5} (x - 8))$

Step 5

Simplify the right side.

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Step 5.1

Simplify $5 (- \frac{2}{5} (x - 8))$ .

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Step 5.1.1

Apply the distributive property.

$5 y - 10 = 5 (- \frac{2}{5} x - \frac{2}{5} \cdot - 8)$

Step 5.1.2

Combine $x$ and $\frac{2}{5}$ .

$5 y - 10 = 5 (- \frac{x \cdot 2}{5} - \frac{2}{5} \cdot - 8)$

Step 5.1.3

Multiply $- \frac{2}{5} \cdot - 8$ .

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Step 5.1.3.1

Multiply $- 8$ by $- 1$ .

$5 y - 10 = 5 (- \frac{x \cdot 2}{5} + 8 (\frac{2}{5}))$

Step 5.1.3.2

Combine $8$ and $\frac{2}{5}$ .

$5 y - 10 = 5 (- \frac{x \cdot 2}{5} + \frac{8 \cdot 2}{5})$

Step 5.1.3.3

Multiply $8$ by $2$ .

$5 y - 10 = 5 (- \frac{x \cdot 2}{5} + \frac{16}{5})$

Step 5.1.4

Move $2$ to the left of $x$ .

$5 y - 10 = 5 (- \frac{2 x}{5} + \frac{16}{5})$

Step 5.1.5

Simplify terms.

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Step 5.1.5.1

Apply the distributive property.

$5 y - 10 = 5 (- \frac{2 x}{5}) + 5 (\frac{16}{5})$

Step 5.1.5.2

Cancel the common factor of $5$ .

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Step 5.1.5.2.1

Move the leading negative in $- \frac{2 x}{5}$ into the numerator.

$5 y - 10 = 5 \frac{- 2 x}{5} + 5 (\frac{16}{5})$

Step 5.1.5.2.2

Cancel the common factor.

$5 y - 10 = 5 \frac{- 2 x}{5} + 5 (\frac{16}{5})$

Step 5.1.5.2.3

Rewrite the expression.

$5 y - 10 = - 2 x + 5 (\frac{16}{5})$

Step 5.1.5.3

Cancel the common factor of $5$ .

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Step 5.1.5.3.1

Cancel the common factor.

$5 y - 10 = - 2 x + 5 (\frac{16}{5})$

Step 5.1.5.3.2

Rewrite the expression.

$5 y - 10 = - 2 x + 16$

Step 6

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

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Step 6.1

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

$5 y - 10 + 2 x = 16$

Step 6.2

Move $- 10$ .

$5 y + 2 x - 10 = 16$

Step 6.3

Reorder $5 y$ and $2 x$ .

$2 x + 5 y - 10 = 16$

Step 7

Move all terms not containing a variable to the right side of the equation.

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Step 7.1

Add $10$ to both sides of the equation.

$2 x + 5 y = 16 + 10$

Step 7.2

Add $16$ and $10$ .

$2 x + 5 y = 26$

Step 8