Pre-Algebra Examples

$2 (x + 1 + 3 (y - 3)) = 2$

Step 1

Solve for $y$ .

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Step 1.1

Divide each term in $2 (x + 1 + 3 (y - 3)) = 2$ by $2$ and simplify.

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Step 1.1.1

Divide each term in $2 (x + 1 + 3 (y - 3)) = 2$ by $2$ .

$\frac{2 (x + 1 + 3 (y - 3))}{2} = \frac{2}{2}$

Step 1.1.2

Simplify the left side.

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Step 1.1.2.1

Cancel the common factor of $2$ .

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Step 1.1.2.1.1

Cancel the common factor.

$\frac{2 (x + 1 + 3 (y - 3))}{2} = \frac{2}{2}$

Step 1.1.2.1.2

Divide $x + 1 + 3 (y - 3)$ by $1$ .

$x + 1 + 3 (y - 3) = \frac{2}{2}$

Step 1.1.2.2

Simplify each term.

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Step 1.1.2.2.1

Apply the distributive property.

$x + 1 + 3 y + 3 \cdot - 3 = \frac{2}{2}$

Step 1.1.2.2.2

Multiply $3$ by $- 3$ .

$x + 1 + 3 y - 9 = \frac{2}{2}$

Step 1.1.2.3

Subtract $9$ from $1$ .

$x + 3 y - 8 = \frac{2}{2}$

Step 1.1.3

Simplify the right side.

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Step 1.1.3.1

Divide $2$ by $2$ .

$x + 3 y - 8 = 1$

Step 1.2

Move all terms not containing $y$ to the right side of the equation.

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Step 1.2.1

Subtract $x$ from both sides of the equation.

$3 y - 8 = 1 - x$

Step 1.2.2

Add $8$ to both sides of the equation.

$3 y = 1 - x + 8$

Step 1.2.3

Add $1$ and $8$ .

$3 y = - x + 9$

Step 1.3

Divide each term in $3 y = - x + 9$ by $3$ and simplify.

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Step 1.3.1

Divide each term in $3 y = - x + 9$ by $3$ .

$\frac{3 y}{3} = \frac{- x}{3} + \frac{9}{3}$

Step 1.3.2

Simplify the left side.

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Step 1.3.2.1

Cancel the common factor of $3$ .

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Step 1.3.2.1.1

Cancel the common factor.

$\frac{3 y}{3} = \frac{- x}{3} + \frac{9}{3}$

Step 1.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{- x}{3} + \frac{9}{3}$

Step 1.3.3

Simplify the right side.

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Step 1.3.3.1

Simplify each term.

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Step 1.3.3.1.1

Move the negative in front of the fraction.

$y = - \frac{x}{3} + \frac{9}{3}$

Step 1.3.3.1.2

Divide $9$ by $3$ .

$y = - \frac{x}{3} + 3$

Step 2

Reorder terms.

$y = - (\frac{1}{3} x) + 3$

Step 3

Remove parentheses.

$y = - \frac{1}{3} x + 3$

Step 4