Basic Math Examples

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

Step 1

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

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Step 1.1

Rewrite.

$0 + 0 + \frac{2}{3} \cdot (x - 4) = \frac{1}{2} \cdot (2 x + 3)$

Step 1.2

Simplify by adding zeros.

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

Step 1.3

Apply the distributive property.

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

Step 1.4

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

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

Step 1.5

Multiply $\frac{2}{3} \cdot - 4$ .

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Step 1.5.1

Combine $\frac{2}{3}$ and $- 4$ .

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

Step 1.5.2

Multiply $2$ by $- 4$ .

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

Step 1.6

Move the negative in front of the fraction.

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

Step 2

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

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Step 2.1

Apply the distributive property.

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

Step 2.2

Cancel the common factor of $2$ .

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Step 2.2.1

Factor $2$ out of $2 x$ .

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

Step 2.2.2

Cancel the common factor.

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

Step 2.2.3

Rewrite the expression.

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

Step 2.3

Combine $\frac{1}{2}$ and $3$ .

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

Step 3

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

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Step 3.1

Subtract $x$ from both sides of the equation.

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

Step 3.2

To write $- x$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{2 x}{3} - x \cdot \frac{3}{3} - \frac{8}{3} = \frac{3}{2}$

Step 3.3

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

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

Step 3.4

Combine the numerators over the common denominator.

$\frac{2 x - x \cdot 3}{3} - \frac{8}{3} = \frac{3}{2}$

Step 3.5

Combine the numerators over the common denominator.

$\frac{2 x - x \cdot 3 - 8}{3} = \frac{3}{2}$

Step 3.6

Multiply $3$ by $- 1$ .

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

Step 3.7

Subtract $3 x$ from $2 x$ .

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

Step 3.8

Factor $- 1$ out of $- x$ .

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

Step 3.9

Rewrite $- 8$ as $- 1 (8)$ .

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

Step 3.10

Factor $- 1$ out of $- (x) - 1 (8)$ .

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

Step 3.11

Rewrite $- (x + 8)$ as $- 1 (x + 8)$ .

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

Step 3.12

Move the negative in front of the fraction.

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

Step 4

Multiply both sides of the equation by $- 3$ .

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

Step 5

Simplify both sides of the equation.

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Step 5.1

Simplify the left side.

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Step 5.1.1

Simplify $- 3 (- \frac{x + 8}{3})$ .

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Step 5.1.1.1

Cancel the common factor of $3$ .

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Step 5.1.1.1.1

Move the leading negative in $- \frac{x + 8}{3}$ into the numerator.

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

Step 5.1.1.1.2

Factor $3$ out of $- 3$ .

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

Step 5.1.1.1.3

Cancel the common factor.

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

Step 5.1.1.1.4

Rewrite the expression.

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

Step 5.1.1.2

Multiply.

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Step 5.1.1.2.1

Multiply $- 1$ by $- 1$ .

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

Step 5.1.1.2.2

Multiply $x + 8$ by $1$ .

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

Step 5.2

Simplify the right side.

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Step 5.2.1

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

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Step 5.2.1.1

Multiply $- 3 (\frac{3}{2})$ .

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Step 5.2.1.1.1

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

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

Step 5.2.1.1.2

Multiply $- 3$ by $3$ .

$x + 8 = \frac{- 9}{2}$

Step 5.2.1.2

Move the negative in front of the fraction.

$x + 8 = - \frac{9}{2}$

Step 6

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

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Step 6.1

Subtract $8$ from both sides of the equation.

$x = - \frac{9}{2} - 8$

Step 6.2

To write $- 8$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$x = - \frac{9}{2} - 8 \cdot \frac{2}{2}$

Step 6.3

Combine $- 8$ and $\frac{2}{2}$ .

$x = - \frac{9}{2} + \frac{- 8 \cdot 2}{2}$

Step 6.4

Combine the numerators over the common denominator.

$x = \frac{- 9 - 8 \cdot 2}{2}$

Step 6.5

Simplify the numerator.

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Step 6.5.1

Multiply $- 8$ by $2$ .

$x = \frac{- 9 - 16}{2}$

Step 6.5.2

Subtract $16$ from $- 9$ .

$x = \frac{- 25}{2}$

Step 6.6

Move the negative in front of the fraction.

$x = - \frac{25}{2}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{25}{2}$

Decimal Form:

$x = - 12.5$

Mixed Number Form:

$x = - 12 \frac{1}{2}$