Algebra Examples

$- 2 (3 a - 2) = \frac{1}{3} (7 - 3 a)$

Step 1

Simplify $- 2 (3 a - 2)$ .

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Step 1.1

Rewrite.

$0 + 0 - 2 (3 a - 2) = \frac{1}{3} \cdot (7 - 3 a)$

Step 1.2

Simplify by adding zeros.

$- 2 (3 a - 2) = \frac{1}{3} \cdot (7 - 3 a)$

Step 1.3

Apply the distributive property.

$- 2 (3 a) - 2 \cdot - 2 = \frac{1}{3} \cdot (7 - 3 a)$

Step 1.4

Multiply.

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Step 1.4.1

Multiply $3$ by $- 2$ .

$- 6 a - 2 \cdot - 2 = \frac{1}{3} \cdot (7 - 3 a)$

Step 1.4.2

Multiply $- 2$ by $- 2$ .

$- 6 a + 4 = \frac{1}{3} \cdot (7 - 3 a)$

Step 2

Simplify $\frac{1}{3} \cdot (7 - 3 a)$ .

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Step 2.1

Apply the distributive property.

$- 6 a + 4 = \frac{1}{3} \cdot 7 + \frac{1}{3} (- 3 a)$

Step 2.2

Combine $\frac{1}{3}$ and $7$ .

$- 6 a + 4 = \frac{7}{3} + \frac{1}{3} (- 3 a)$

Step 2.3

Cancel the common factor of $3$ .

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Step 2.3.1

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

$- 6 a + 4 = \frac{7}{3} + \frac{1}{3} (3 (- a))$

Step 2.3.2

Cancel the common factor.

$- 6 a + 4 = \frac{7}{3} + \frac{1}{3} (3 (- a))$

Step 2.3.3

Rewrite the expression.

$- 6 a + 4 = \frac{7}{3} - a$

Step 3

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

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Step 3.1

Add $a$ to both sides of the equation.

$- 6 a + 4 + a = \frac{7}{3}$

Step 3.2

Add $- 6 a$ and $a$ .

$- 5 a + 4 = \frac{7}{3}$

Step 4

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

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Step 4.1

Subtract $4$ from both sides of the equation.

$- 5 a = \frac{7}{3} - 4$

Step 4.2

To write $- 4$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- 5 a = \frac{7}{3} - 4 \cdot \frac{3}{3}$

Step 4.3

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

$- 5 a = \frac{7}{3} + \frac{- 4 \cdot 3}{3}$

Step 4.4

Combine the numerators over the common denominator.

$- 5 a = \frac{7 - 4 \cdot 3}{3}$

Step 4.5

Simplify the numerator.

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Step 4.5.1

Multiply $- 4$ by $3$ .

$- 5 a = \frac{7 - 12}{3}$

Step 4.5.2

Subtract $12$ from $7$ .

$- 5 a = \frac{- 5}{3}$

Step 4.6

Move the negative in front of the fraction.

$- 5 a = - \frac{5}{3}$

Step 5

Divide each term in $- 5 a = - \frac{5}{3}$ by $- 5$ and simplify.

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Step 5.1

Divide each term in $- 5 a = - \frac{5}{3}$ by $- 5$ .

$\frac{- 5 a}{- 5} = \frac{- \frac{5}{3}}{- 5}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $- 5$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{- 5 a}{- 5} = \frac{- \frac{5}{3}}{- 5}$

Step 5.2.1.2

Divide $a$ by $1$ .

$a = \frac{- \frac{5}{3}}{- 5}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Multiply the numerator by the reciprocal of the denominator.

$a = - \frac{5}{3} \cdot \frac{1}{- 5}$

Step 5.3.2

Cancel the common factor of $5$ .

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Step 5.3.2.1

Move the leading negative in $- \frac{5}{3}$ into the numerator.

$a = \frac{- 5}{3} \cdot \frac{1}{- 5}$

Step 5.3.2.2

Factor $5$ out of $- 5$ .

$a = \frac{5 (- 1)}{3} \cdot \frac{1}{- 5}$

Step 5.3.2.3

Factor $5$ out of $- 5$ .

$a = \frac{5 \cdot - 1}{3} \cdot \frac{1}{5 \cdot - 1}$

Step 5.3.2.4

Cancel the common factor.

$a = \frac{5 \cdot - 1}{3} \cdot \frac{1}{5 \cdot - 1}$

Step 5.3.2.5

Rewrite the expression.

$a = \frac{- 1}{3} \cdot \frac{1}{- 1}$

Step 5.3.3

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

$a = \frac{- 1}{3 \cdot - 1}$

Step 5.3.4

Multiply $3$ by $- 1$ .

$a = \frac{- 1}{- 3}$

Step 5.3.5

Dividing two negative values results in a positive value.

$a = \frac{1}{3}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$a = \frac{1}{3}$

Decimal Form:

$a = 0.\overline{3}$