Finite Math Examples

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

Step 1

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

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Step 1.1

Rewrite.

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

Step 1.2

Simplify by adding zeros.

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

Step 1.3

Apply the distributive property.

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

Step 1.4

Multiply $\frac{1}{3} (2 x)$ .

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Step 1.4.1

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

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

Step 1.4.2

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

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

Step 1.5

Cancel the common factor of $3$ .

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Step 1.5.1

Factor $3$ out of $- 3 a$ .

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

Step 1.5.2

Cancel the common factor.

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

Step 1.5.3

Rewrite the expression.

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

Step 2

Apply the distributive property.

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

Step 3

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

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Step 3.1

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

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

Step 3.2

To write $- 2 x$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

Step 3.3

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

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

Step 3.4

Combine the numerators over the common denominator.

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

Step 3.5

Simplify each term.

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Step 3.5.1

Simplify the numerator.

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Step 3.5.1.1

Factor $2 x$ out of $2 x - 2 x \cdot 3$ .

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Step 3.5.1.1.1

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

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

Step 3.5.1.1.2

Factor $2 x$ out of $- 2 x \cdot 3$ .

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

Step 3.5.1.1.3

Factor $2 x$ out of $2 x (1) + 2 x (- 1 \cdot 3)$ .

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

Step 3.5.1.2

Multiply $- 1$ by $3$ .

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

Step 3.5.1.3

Subtract $3$ from $1$ .

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

Step 3.5.1.4

Multiply $- 2$ by $2$ .

$- a + \frac{- 4 x}{3} = 2 a$

Step 3.5.2

Move the negative in front of the fraction.

$- a - \frac{4 x}{3} = 2 a$

Step 4

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

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Step 4.1

Add $a$ to both sides of the equation.

$- \frac{4 x}{3} = 2 a + a$

Step 4.2

Add $2 a$ and $a$ .

$- \frac{4 x}{3} = 3 a$

Step 5

Multiply both sides of the equation by $- \frac{3}{4}$ .

$- \frac{3}{4} (- \frac{4 x}{3}) = - \frac{3}{4} (3 a)$

Step 6

Simplify both sides of the equation.

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Step 6.1

Simplify the left side.

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Step 6.1.1

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

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Step 6.1.1.1

Cancel the common factor of $3$ .

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Step 6.1.1.1.1

Move the leading negative in $- \frac{3}{4}$ into the numerator.

$\frac{- 3}{4} (- \frac{4 x}{3}) = - \frac{3}{4} (3 a)$

Step 6.1.1.1.2

Move the leading negative in $- \frac{4 x}{3}$ into the numerator.

$\frac{- 3}{4} \cdot \frac{- 4 x}{3} = - \frac{3}{4} (3 a)$

Step 6.1.1.1.3

Factor $3$ out of $- 3$ .

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

Step 6.1.1.1.4

Cancel the common factor.

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

Step 6.1.1.1.5

Rewrite the expression.

$\frac{- 1}{4} (- 4 x) = - \frac{3}{4} (3 a)$

Step 6.1.1.2

Cancel the common factor of $4$ .

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Step 6.1.1.2.1

Factor $4$ out of $- 4 x$ .

$\frac{- 1}{4} (4 (- x)) = - \frac{3}{4} (3 a)$

Step 6.1.1.2.2

Cancel the common factor.

$\frac{- 1}{4} (4 (- x)) = - \frac{3}{4} (3 a)$

Step 6.1.1.2.3

Rewrite the expression.

$- - x = - \frac{3}{4} (3 a)$

Step 6.1.1.3

Multiply.

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Step 6.1.1.3.1

Multiply $- 1$ by $- 1$ .

$1 x = - \frac{3}{4} (3 a)$

Step 6.1.1.3.2

Multiply $x$ by $1$ .

$x = - \frac{3}{4} (3 a)$

Step 6.2

Simplify the right side.

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Step 6.2.1

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

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Step 6.2.1.1

Multiply $- \frac{3}{4} (3 a)$ .

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Step 6.2.1.1.1

Multiply $3$ by $- 1$ .

$x = - 3 (\frac{3}{4}) a$

Step 6.2.1.1.2

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

$x = \frac{- 3 \cdot 3}{4} a$

Step 6.2.1.1.3

Multiply $- 3$ by $3$ .

$x = \frac{- 9}{4} a$

Step 6.2.1.1.4

Combine $\frac{- 9}{4}$ and $a$ .

$x = \frac{- 9 a}{4}$

Step 6.2.1.2

Move the negative in front of the fraction.

$x = - \frac{9 a}{4}$