Pre-Algebra Examples

$\frac{1}{2} \cdot (x + 6) = \frac{3}{2} x - 1$

Step 1

Simplify $\frac{1}{2} \cdot (x + 6)$ .

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Step 1.1

Rewrite.

$0 + 0 + \frac{1}{2} \cdot (x + 6) = \frac{3}{2} x - 1$

Step 1.2

Simplify by adding zeros.

$\frac{1}{2} \cdot (x + 6) = \frac{3}{2} x - 1$

Step 1.3

Apply the distributive property.

$\frac{1}{2} x + \frac{1}{2} \cdot 6 = \frac{3}{2} x - 1$

Step 1.4

Combine $\frac{1}{2}$ and $x$ .

$\frac{x}{2} + \frac{1}{2} \cdot 6 = \frac{3}{2} x - 1$

Step 1.5

Cancel the common factor of $2$ .

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Step 1.5.1

Factor $2$ out of $6$ .

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

Step 1.5.2

Cancel the common factor.

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

Step 1.5.3

Rewrite the expression.

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

Step 2

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

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

Step 3

Move all terms containing $x$ to the left side of the equation.

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Step 3.1

Subtract $\frac{3 x}{2}$ from both sides of the equation.

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

Step 3.2

Combine the numerators over the common denominator.

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

Step 3.3

Subtract $3 x$ from $x$ .

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

Step 3.4

Cancel the common factor of $- 2$ and $2$ .

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Step 3.4.1

Factor $2$ out of $- 2 x$ .

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

Step 3.4.2

Cancel the common factors.

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Step 3.4.2.1

Factor $2$ out of $2$ .

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

Step 3.4.2.2

Cancel the common factor.

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

Step 3.4.2.3

Rewrite the expression.

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

Step 3.4.2.4

Divide $- x$ by $1$ .

$3 - x = - 1$

Step 4

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

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Step 4.1

Subtract $3$ from both sides of the equation.

$- x = - 1 - 3$

Step 4.2

Subtract $3$ from $- 1$ .

$- x = - 4$

Step 5

Divide each term in $- x = - 4$ by $- 1$ and simplify.

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Step 5.1

Divide each term in $- x = - 4$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- 4}{- 1}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{- 4}{- 1}$

Step 5.2.2

Divide $x$ by $1$ .

$x = \frac{- 4}{- 1}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Divide $- 4$ by $- 1$ .

$x = 4$