Finite Math Examples

$y = - \frac{5}{2} x - 5$

Step 1

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

Step 2

Multiply both sides by $2$ .

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

Step 3

Simplify the right side.

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Step 3.1

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

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Step 3.1.1

Simplify each term.

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Step 3.1.1.1

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

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

Step 3.1.1.2

Move $5$ to the left of $x$ .

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

Step 3.1.2

Simplify terms.

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Step 3.1.2.1

Apply the distributive property.

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

Step 3.1.2.2

Cancel the common factor of $2$ .

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Step 3.1.2.2.1

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

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

Step 3.1.2.2.2

Cancel the common factor.

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

Step 3.1.2.2.3

Rewrite the expression.

$2 y = - 5 x + 2 \cdot - 5$

Step 3.1.2.3

Multiply $2$ by $- 5$ .

$2 y = - 5 x - 10$

Step 4

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

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Step 4.1

Add $5 x$ to both sides of the equation.

$2 y + 5 x = - 10$

Step 4.2

Reorder $2 y$ and $5 x$ .

$5 x + 2 y = - 10$

Step 5