Pre-Algebra Examples

$y - 6.4 x = - 4$

Step 1

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

Step 2

Change $- 6.4$ into a fraction.

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Step 2.1

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

$y + \frac{10 \cdot - 6.4}{10} x = - 4$

Step 2.2

Multiply $10$ by $- 6.4$ .

$y + \frac{- 64}{10} x = - 4$

Step 2.3

Move the negative in front of the fraction.

$y - \frac{64}{10} x = - 4$

Step 2.4

Cancel the common factor of $64$ and $10$ .

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Step 2.4.1

Factor $2$ out of $64$ .

$y - \frac{2 (32)}{10} x = - 4$

Step 2.4.2

Cancel the common factors.

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Step 2.4.2.1

Factor $2$ out of $10$ .

$y - \frac{2 \cdot 32}{2 \cdot 5} x = - 4$

Step 2.4.2.2

Cancel the common factor.

$y - \frac{2 \cdot 32}{2 \cdot 5} x = - 4$

Step 2.4.2.3

Rewrite the expression.

$y - \frac{32}{5} x = - 4$

Step 3

Multiply both sides by $5$ .

$5 (y - \frac{32}{5} x) = 5 \cdot - 4$

Step 4

Simplify the left side.

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Step 4.1

Simplify $5 (y - \frac{32}{5} x)$ .

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Step 4.1.1

Simplify each term.

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Step 4.1.1.1

Combine $x$ and $\frac{32}{5}$ .

$5 (y - \frac{x \cdot 32}{5}) = 5 \cdot - 4$

Step 4.1.1.2

Move $32$ to the left of $x$ .

$5 (y - \frac{32 x}{5}) = 5 \cdot - 4$

Step 4.1.2

Simplify terms.

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Step 4.1.2.1

Apply the distributive property.

$5 y + 5 (- \frac{32 x}{5}) = 5 \cdot - 4$

Step 4.1.2.2

Cancel the common factor of $5$ .

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Step 4.1.2.2.1

Move the leading negative in $- \frac{32 x}{5}$ into the numerator.

$5 y + 5 \frac{- 32 x}{5} = 5 \cdot - 4$

Step 4.1.2.2.2

Cancel the common factor.

$5 y + 5 \frac{- 32 x}{5} = 5 \cdot - 4$

Step 4.1.2.2.3

Rewrite the expression.

$5 y - 32 x = 5 \cdot - 4$

Step 5

Simplify the right side.

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Step 5.1

Multiply $5$ by $- 4$ .

$5 y - 32 x = - 20$

Step 6

Rewrite the equation.

$- 20 = 5 y - 32 x$

Step 7

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

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Step 7.1

Subtract $5 y$ from both sides of the equation.

$- 20 - 5 y = - 32 x$

Step 7.2

Add $32 x$ to both sides of the equation.

$- 20 - 5 y + 32 x = 0$

Step 7.3

Move $- 20$ .

$- 5 y + 32 x - 20 = 0$

Step 7.4

Reorder $- 5 y$ and $32 x$ .

$32 x - 5 y - 20 = 0$

Step 8

Add $20$ to both sides of the equation.

$32 x - 5 y = 20$

Step 9