Algebra Examples

$y + 7 = - \frac{2}{5} (x - 10)$

Step 1

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

Step 2

Multiply both sides by $5$ .

$5 (y + 7) = 5 (- \frac{2}{5} (x - 10))$

Step 3

Simplify the left side.

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Step 3.1

Simplify $5 (y + 7)$ .

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Step 3.1.1

Apply the distributive property.

$5 y + 5 \cdot 7 = 5 (- \frac{2}{5} (x - 10))$

Step 3.1.2

Multiply $5$ by $7$ .

$5 y + 35 = 5 (- \frac{2}{5} (x - 10))$

Step 4

Simplify the right side.

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Step 4.1

Simplify $5 (- \frac{2}{5} (x - 10))$ .

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Step 4.1.1

Simplify terms.

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Step 4.1.1.1

Apply the distributive property.

$5 y + 35 = 5 (- \frac{2}{5} x - \frac{2}{5} \cdot - 10)$

Step 4.1.1.2

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

$5 y + 35 = 5 (- \frac{x \cdot 2}{5} - \frac{2}{5} \cdot - 10)$

Step 4.1.1.3

Cancel the common factor of $5$ .

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Step 4.1.1.3.1

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

$5 y + 35 = 5 (- \frac{x \cdot 2}{5} + \frac{- 2}{5} \cdot - 10)$

Step 4.1.1.3.2

Factor $5$ out of $- 10$ .

$5 y + 35 = 5 (- \frac{x \cdot 2}{5} + \frac{- 2}{5} \cdot (5 (- 2)))$

Step 4.1.1.3.3

Cancel the common factor.

$5 y + 35 = 5 (- \frac{x \cdot 2}{5} + \frac{- 2}{5} \cdot (5 \cdot - 2))$

Step 4.1.1.3.4

Rewrite the expression.

$5 y + 35 = 5 (- \frac{x \cdot 2}{5} - 2 \cdot - 2)$

Step 4.1.1.4

Multiply $- 2$ by $- 2$ .

$5 y + 35 = 5 (- \frac{x \cdot 2}{5} + 4)$

Step 4.1.2

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

$5 y + 35 = 5 (- \frac{2 x}{5} + 4)$

Step 4.1.3

Simplify terms.

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Step 4.1.3.1

Apply the distributive property.

$5 y + 35 = 5 (- \frac{2 x}{5}) + 5 \cdot 4$

Step 4.1.3.2

Cancel the common factor of $5$ .

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Step 4.1.3.2.1

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

$5 y + 35 = 5 \frac{- 2 x}{5} + 5 \cdot 4$

Step 4.1.3.2.2

Cancel the common factor.

$5 y + 35 = 5 \frac{- 2 x}{5} + 5 \cdot 4$

Step 4.1.3.2.3

Rewrite the expression.

$5 y + 35 = - 2 x + 5 \cdot 4$

Step 4.1.3.3

Multiply $5$ by $4$ .

$5 y + 35 = - 2 x + 20$

Step 5

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

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Step 5.1

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

$5 y + 35 + 2 x = 20$

Step 5.2

Move $35$ .

$5 y + 2 x + 35 = 20$

Step 5.3

Reorder $5 y$ and $2 x$ .

$2 x + 5 y + 35 = 20$

Step 6

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

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Step 6.1

Subtract $35$ from both sides of the equation.

$2 x + 5 y = 20 - 35$

Step 6.2

Subtract $35$ from $20$ .

$2 x + 5 y = - 15$

Step 7