Pre-Algebra Examples

$y + 5 = 1.5 (x - 4)$

Step 1

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

Step 2

Change $1.5$ into a fraction.

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Step 2.1

Multiply by $\frac{10}{10}$ to remove the decimal.

$y + 5 = \frac{10 \cdot 1.5}{10} (x - 4)$

Step 2.2

Multiply $10$ by $1.5$ .

$y + 5 = \frac{15}{10} (x - 4)$

Step 2.3

Cancel the common factor of $15$ and $10$ .

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Step 2.3.1

Factor $5$ out of $15$ .

$y + 5 = \frac{5 (3)}{10} (x - 4)$

Step 2.3.2

Cancel the common factors.

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Step 2.3.2.1

Factor $5$ out of $10$ .

$y + 5 = \frac{5 \cdot 3}{5 \cdot 2} (x - 4)$

Step 2.3.2.2

Cancel the common factor.

$y + 5 = \frac{5 \cdot 3}{5 \cdot 2} (x - 4)$

Step 2.3.2.3

Rewrite the expression.

$y + 5 = \frac{3}{2} (x - 4)$

Step 3

Multiply both sides by $2$ .

$2 (y + 5) = 2 (\frac{3}{2} (x - 4))$

Step 4

Simplify the left side.

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Step 4.1

Simplify $2 (y + 5)$ .

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Step 4.1.1

Apply the distributive property.

$2 y + 2 \cdot 5 = 2 (\frac{3}{2} (x - 4))$

Step 4.1.2

Multiply $2$ by $5$ .

$2 y + 10 = 2 (\frac{3}{2} (x - 4))$

Step 5

Simplify the right side.

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Step 5.1

Simplify $2 (\frac{3}{2} (x - 4))$ .

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Step 5.1.1

Apply the distributive property.

$2 y + 10 = 2 (\frac{3}{2} x + \frac{3}{2} \cdot - 4)$

Step 5.1.2

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

$2 y + 10 = 2 (\frac{3 x}{2} + \frac{3}{2} \cdot - 4)$

Step 5.1.3

Cancel the common factor of $2$ .

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Step 5.1.3.1

Factor $2$ out of $- 4$ .

$2 y + 10 = 2 (\frac{3 x}{2} + \frac{3}{2} \cdot (2 (- 2)))$

Step 5.1.3.2

Cancel the common factor.

$2 y + 10 = 2 (\frac{3 x}{2} + \frac{3}{2} \cdot (2 \cdot - 2))$

Step 5.1.3.3

Rewrite the expression.

$2 y + 10 = 2 (\frac{3 x}{2} + 3 \cdot - 2)$

Step 5.1.4

Multiply $3$ by $- 2$ .

$2 y + 10 = 2 (\frac{3 x}{2} - 6)$

Step 5.1.5

Apply the distributive property.

$2 y + 10 = 2 \frac{3 x}{2} + 2 \cdot - 6$

Step 5.1.6

Cancel the common factor of $2$ .

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Step 5.1.6.1

Cancel the common factor.

$2 y + 10 = 2 \frac{3 x}{2} + 2 \cdot - 6$

Step 5.1.6.2

Rewrite the expression.

$2 y + 10 = 3 x + 2 \cdot - 6$

Step 5.1.7

Multiply $2$ by $- 6$ .

$2 y + 10 = 3 x - 12$

Step 6

Rewrite the equation.

$3 x - 12 = 2 y + 10$

Step 7

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

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Step 7.1

Subtract $2 y$ from both sides of the equation.

$3 x - 12 - 2 y = 10$

Step 7.2

Move $- 12$ .

$3 x - 2 y - 12 = 10$

Step 8

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

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Step 8.1

Add $12$ to both sides of the equation.

$3 x - 2 y = 10 + 12$

Step 8.2

Add $10$ and $12$ .

$3 x - 2 y = 22$

Step 9