Pre-Algebra Examples

$y - (4) = - \frac{3}{2} \cdot (x - 1)$

Step 1

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

Step 2

Multiply both sides by $2$ .

$2 (y - (4)) = 2 (- \frac{3}{2} \cdot (x - 1))$

Step 3

Simplify the left side.

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Step 3.1

Simplify $2 (y - (4))$ .

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Step 3.1.1

Multiply $- 1$ by $4$ .

$2 (y - 4) = 2 (- \frac{3}{2} \cdot (x - 1))$

Step 3.1.2

Apply the distributive property.

$2 y + 2 \cdot - 4 = 2 (- \frac{3}{2} \cdot (x - 1))$

Step 3.1.3

Multiply $2$ by $- 4$ .

$2 y - 8 = 2 (- \frac{3}{2} \cdot (x - 1))$

Step 4

Simplify the right side.

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Step 4.1

Simplify $2 (- \frac{3}{2} \cdot (x - 1))$ .

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Step 4.1.1

Apply the distributive property.

$2 y - 8 = 2 (- \frac{3}{2} x - \frac{3}{2} \cdot - 1)$

Step 4.1.2

Combine $x$ and $\frac{3}{2}$ .

$2 y - 8 = 2 (- \frac{x \cdot 3}{2} - \frac{3}{2} \cdot - 1)$

Step 4.1.3

Multiply $- \frac{3}{2} \cdot - 1$ .

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Step 4.1.3.1

Multiply $- 1$ by $- 1$ .

$2 y - 8 = 2 (- \frac{x \cdot 3}{2} + 1 (\frac{3}{2}))$

Step 4.1.3.2

Multiply $\frac{3}{2}$ by $1$ .

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

Step 4.1.4

Move $3$ to the left of $x$ .

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

Step 4.1.5

Simplify terms.

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Step 4.1.5.1

Apply the distributive property.

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

Step 4.1.5.2

Cancel the common factor of $2$ .

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Step 4.1.5.2.1

Move the leading negative in $- \frac{3 x}{2}$ into the numerator.

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

Step 4.1.5.2.2

Cancel the common factor.

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

Step 4.1.5.2.3

Rewrite the expression.

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

Step 4.1.5.3

Cancel the common factor of $2$ .

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Step 4.1.5.3.1

Cancel the common factor.

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

Step 4.1.5.3.2

Rewrite the expression.

$2 y - 8 = - 3 x + 3$

Step 5

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

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Step 5.1

Add $3 x$ to both sides of the equation.

$2 y - 8 + 3 x = 3$

Step 5.2

Move $- 8$ .

$2 y + 3 x - 8 = 3$

Step 5.3

Reorder $2 y$ and $3 x$ .

$3 x + 2 y - 8 = 3$

Step 6

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

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Step 6.1

Add $8$ to both sides of the equation.

$3 x + 2 y = 3 + 8$

Step 6.2

Add $3$ and $8$ .

$3 x + 2 y = 11$

Step 7