Algebra Examples

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

Step 1

Multiply both sides by $- 3$ .

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

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $\frac{3 a - 2}{- 3} \cdot - 3$ .

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Step 2.1.1.1

Cancel the common factor of $3$ .

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Step 2.1.1.1.1

Factor $3$ out of $- 3$ .

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

Step 2.1.1.1.2

Factor $3$ out of $- 3$ .

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

Step 2.1.1.1.3

Cancel the common factor.

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

Step 2.1.1.1.4

Rewrite the expression.

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

Step 2.1.1.2

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

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

Step 2.1.1.3

Simplify the expression.

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Step 2.1.1.3.1

Move the negative one from the denominator of $\frac{(3 a - 2) \cdot - 1}{- 1}$ .

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

Step 2.1.1.3.2

Rewrite $- 1 \cdot ((3 a - 2) \cdot - 1)$ as $- ((3 a - 2) \cdot - 1)$ .

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

Step 2.1.1.4

Apply the distributive property.

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

Step 2.1.1.5

Multiply.

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Step 2.1.1.5.1

Multiply $- 1$ by $3$ .

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

Step 2.1.1.5.2

Multiply $- 2$ by $- 1$ .

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

Step 2.1.1.6

Apply the distributive property.

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

Step 2.1.1.7

Multiply.

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Step 2.1.1.7.1

Multiply $- 3$ by $- 1$ .

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

Step 2.1.1.7.2

Multiply $- 1$ by $2$ .

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

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $\frac{a}{3} \cdot - 3$ .

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Step 2.2.1.1

Cancel the common factor of $3$ .

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Step 2.2.1.1.1

Factor $3$ out of $- 3$ .

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

Step 2.2.1.1.2

Cancel the common factor.

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

Step 2.2.1.1.3

Rewrite the expression.

$3 a - 2 = a \cdot - 1$

Step 2.2.1.2

Simplify the expression.

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Step 2.2.1.2.1

Move $- 1$ to the left of $a$ .

$3 a - 2 = - 1 \cdot a$

Step 2.2.1.2.2

Rewrite $- 1 a$ as $- a$ .

$3 a - 2 = - a$

Step 3

Solve for $a$ .

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Step 3.1

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

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Step 3.1.1

Add $a$ to both sides of the equation.

$3 a - 2 + a = 0$

Step 3.1.2

Add $3 a$ and $a$ .

$4 a - 2 = 0$

Step 3.2

Add $2$ to both sides of the equation.

$4 a = 2$

Step 3.3

Divide each term in $4 a = 2$ by $4$ and simplify.

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Step 3.3.1

Divide each term in $4 a = 2$ by $4$ .

$\frac{4 a}{4} = \frac{2}{4}$

Step 3.3.2

Simplify the left side.

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Step 3.3.2.1

Cancel the common factor of $4$ .

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Step 3.3.2.1.1

Cancel the common factor.

$\frac{4 a}{4} = \frac{2}{4}$

Step 3.3.2.1.2

Divide $a$ by $1$ .

$a = \frac{2}{4}$

Step 3.3.3

Simplify the right side.

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Step 3.3.3.1

Cancel the common factor of $2$ and $4$ .

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Step 3.3.3.1.1

Factor $2$ out of $2$ .

$a = \frac{2 (1)}{4}$

Step 3.3.3.1.2

Cancel the common factors.

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Step 3.3.3.1.2.1

Factor $2$ out of $4$ .

$a = \frac{2 \cdot 1}{2 \cdot 2}$

Step 3.3.3.1.2.2

Cancel the common factor.

$a = \frac{2 \cdot 1}{2 \cdot 2}$

Step 3.3.3.1.2.3

Rewrite the expression.

$a = \frac{1}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$a = \frac{1}{2}$

Decimal Form:

$a = 0.5$