Pre-Algebra Examples

$y - (- 7) = \frac{1}{7} \cdot (x - (- 7))$

Step 1

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

Step 2

Multiply both sides by $7$ .

$7 (y - (- 7)) = 7 (\frac{1}{7} \cdot (x - (- 7)))$

Step 3

Simplify the left side.

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Step 3.1

Simplify $7 (y - (- 7))$ .

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Step 3.1.1

Multiply $- 1$ by $- 7$ .

$7 (y + 7) = 7 (\frac{1}{7} \cdot (x - (- 7)))$

Step 3.1.2

Apply the distributive property.

$7 y + 7 \cdot 7 = 7 (\frac{1}{7} \cdot (x - (- 7)))$

Step 3.1.3

Multiply $7$ by $7$ .

$7 y + 49 = 7 (\frac{1}{7} \cdot (x - (- 7)))$

Step 4

Simplify the right side.

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Step 4.1

Simplify $7 (\frac{1}{7} \cdot (x - (- 7)))$ .

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Step 4.1.1

Multiply $- 1$ by $- 7$ .

$7 y + 49 = 7 (\frac{1}{7} \cdot (x + 7))$

Step 4.1.2

Apply the distributive property.

$7 y + 49 = 7 (\frac{1}{7} x + \frac{1}{7} \cdot 7)$

Step 4.1.3

Combine $\frac{1}{7}$ and $x$ .

$7 y + 49 = 7 (\frac{x}{7} + \frac{1}{7} \cdot 7)$

Step 4.1.4

Cancel the common factor of $7$ .

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Step 4.1.4.1

Cancel the common factor.

$7 y + 49 = 7 (\frac{x}{7} + \frac{1}{7} \cdot 7)$

Step 4.1.4.2

Rewrite the expression.

$7 y + 49 = 7 (\frac{x}{7} + 1)$

Step 4.1.5

Apply the distributive property.

$7 y + 49 = 7 \frac{x}{7} + 7 \cdot 1$

Step 4.1.6

Cancel the common factor of $7$ .

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Step 4.1.6.1

Cancel the common factor.

$7 y + 49 = 7 \frac{x}{7} + 7 \cdot 1$

Step 4.1.6.2

Rewrite the expression.

$7 y + 49 = x + 7 \cdot 1$

Step 4.1.7

Multiply $7$ by $1$ .

$7 y + 49 = x + 7$

Step 5

Rewrite the equation.

$x + 7 = 7 y + 49$

Step 6

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

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Step 6.1

Subtract $7 y$ from both sides of the equation.

$x + 7 - 7 y = 49$

Step 6.2

Move $7$ .

$x - 7 y + 7 = 49$

Step 7

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

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Step 7.1

Subtract $7$ from both sides of the equation.

$x - 7 y = 49 - 7$

Step 7.2

Subtract $7$ from $49$ .

$x - 7 y = 42$

Step 8